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We're on problem 33 and it asks, which equation

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represents a line that is parallel to y is equal to

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minus 5/4 x plus 2?

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So a line that's parallel will have the same slope.

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And we can just look at this, we could inspect this and say,

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OK, the slope of this line is the coefficient on the x term.

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So slope on this line is right there.

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Because the slope is equal to minus 5/4.

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And so we just have to look at the other choices and say,

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which one has the same slope of minus 5/4?

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And choice A actually is, choice A is y is equal to

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minus 5/4 x plus 1.

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So it has the exact same slope and it's just

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shifted down by 1.

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So A is our choice.

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Now problem 34.

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Let me copy and paste this one.

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Let's see, I can paste it.

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All right, and they ask us, which graph represents the

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solution to this system of inequalities?

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OK, so we could take each of these inequalities and then,

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what we want to do is we want the area that satisfies both

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of these inequalities.

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So let's take a look at the first one.

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And I like to always have it in kind of y is equal to mx

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plus b form.

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So let's do that.

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So the first one says 2x is greater than or

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equal to y minus 1.

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If we add 1 to both sides, we get 2x plus 1 is greater than

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or equal to y.

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And if we just want to write that in a way that we're used

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to seeing it, y-- I'm just switching it around.

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y is less than or equal to 2x plus 1.

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So let's see which one this represents.

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We have a line, 2x plus 1, so the y-intercept is 1 and the

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slope is 2.

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So let's see.

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So that's this line here.

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y-intercept 1 and if we go over to the

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right 2, we go up 4.

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However much we increase in x, we increase twice

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as much with y.

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That's what the slope tells us.

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And that's this line in this chart like that.

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Fair enough.

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So that's that line.

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And they're saying y is less than that.

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So we want the area below that graph.

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So it's not this one.

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This one they're shading in the area above that line.

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For any x and y that's on the line, they're shading in y is

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greater than that point.

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No, but we what y is less than that point.

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For any y on the point, all the y's less

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than it satisfy it.

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So based on the information now, this one seems to be a

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pretty good candidate.

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I haven't looked at the other line yet.

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And frankly, neither of-- I guess, no neither.

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Maybe this one might be a candidate because this

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is also less than.

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Maybe we have to be less than both of these lines, right?

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This is the line that we just figured out.

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We're definitely less than it.

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Maybe we have to be less than that second line as well.

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So if we have to be greater than that second line, we

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haven't looked at that yet.

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It's going to be choice C.

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If we have to be less than the second line and this first

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line, then we're going to be in choice D.

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Let's see what the second piece of information tells us.

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OK, well they actually have a typo and they don't give us

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enough information to actually-- let

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me look up the answer.

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Because they didn't even write a greater than or equal or

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nothing here.

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So I have to see what they probably intended.

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OK, so I just looked up the answer and they said that the

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answer is C.

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So they must want us to be greater than this second line.

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So let's figure out what this should have been.

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What should have this-- should there have been an equals?

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Well, definitely not an equal sign.

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But should there have been a greater than or

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less than or whatever?

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We'll figure that out.

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So let's see.

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2x minus 5y circle 10.

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We don't know if there's an equal there or less-- this is

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almost a better exercise than what they intended.

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Let's see.

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If we were to add 5y to both sides, I just want to get y on

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the other side.

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And I don't want to have to say flip signs and

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divide by minus 5.

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So let me get 5y on the other side.

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So I'll add 5y to both sides.

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So we get 2x.

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Whatever inequality sign, so that could

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be an equal or whatever.

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10 plus 5y.

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Subtract 10 from both sides.

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So you get 2x minus 10 circle 5y.

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Remember that circle could be an equal sign.

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Well, it's not an equal.

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It's either a greater than or equal or it's a

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less than or equal.

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And then we can divide both sides by 5 and you get 2

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divided by 5 x minus 2, some greater than or equal or less

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than or equal sign, y.

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Now they told us C was the answer because I had to look

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it up because they didn't give us any inequality sign there.

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If C is the answer that means we're going to-- we want all

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y's that are below the first line.

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So below this line right here.

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So that's that area.

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And if we're in this grey area, all y's that are above

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this bottom line.

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So if we're above this bottom line, this bottom line

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is 2/5 x minus 2.

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So we want all y's that are greater than that.

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Sorry, I've done it-- we want all the y's that are greater

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than that. y is greater than this thing.

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So that sign in this problem should have

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been a less than sign.

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I'm saying y is greater than this.

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But if you read it left to right, you have 2x minus 2 is

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less than y.

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And so we figured out the sign.

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And you might be saying, hey, wait.

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How come this area over here doesn't work?

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Well if you think about it, this area is

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above our first line.

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This area is y is greater than 2x plus 1.

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It's above our first line.

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And it's actually below our second line.

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So it's actually the opposite area.

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Anyway, next problem.

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The answer was C.

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Next problem, 35.

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OK, let's see.

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I'll copy and paste this one.

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I think the choices are interesting.

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What is the solution to this system of equations?

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All right, so let's see if we can get in a form that makes

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it easy to look at.

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Let's take that first equation and let's

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add 3x to both sides.

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If you add 3x to both sides, that first equation becomes

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positive 3x plus y is equal to minus 2.

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All I did is I did plus 3-- you can't see that.

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I added plus 3x to both sides of this equation.

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And of course, that cancels with that.

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All right, and now let' see.

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That second equation is 6x plus 2 is equal to minus 2.

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Well let me do something else to this equation and I think

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it'll become apparent that these are

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actually the same line.

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So if you take this first equation and multiply both

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sides of it by 2, what do you get?

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Let's see.

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Multiply 3x plus y by 2, you get 2 times 3x is 6x.

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Plus 2 times y.

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You have to distribute the 2.

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Plus 2y is equal to.

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Minus 2 times to 2 is minus 4.

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And they're the same line.

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So when you're solving a system of equations, you're

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figuring out, where do those two equations intersect?

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If they're the same lines, they intersect everywhere.

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So they have an infinite number of solutions.

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So the answer is choice D.

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Next problem.

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They give us another one like that.

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They want to know the ordered pair that's a

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solution to this equation.

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I'll just copy and paste the equation there.

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OK, so the easiest thing to do is probably to just subtract

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the second equation from the first equation.

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And instead, I'll actually write it out explicitly.

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So the first question is x plus 3y is equal to 7.

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Instead of subtracting this one from that one, let's just

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multiply the second question by negative 1 and then we'll

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add the two equations.

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So if we multiply this bottom equation by negative 1 we get

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minus x minus 2y is equal to minus 10.

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And the whole reason why I'm doing that is I know when I

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add these two left-hand sides, the x and the minus x are

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going to cancel out.

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And then I can just solve for y.

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That's why you immediately see, they have an x and an x.

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If we subtract this from that, they'll cancel out.

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So if we add these two equations, the x' cancel out.

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3y minus 2y is equal to y.

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And 7 minus 10 is equal to minus 3.

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Fair enough.

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00:09:25,559 --> 00:09:27,500
And now we can substitute back in to figure out an x.

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So let's use the first equation.

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00:09:30,895 --> 00:09:36,129
x plus 3 times minus 3-- we figured out what y is-- is

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equal to 7.

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00:09:39,250 --> 00:09:41,200
And then you get x.

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00:09:41,200 --> 00:09:44,485
3 times-- minus 9 is equal to 7.

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00:09:44,485 --> 00:09:47,620
x is equal to-- add 9 to both sides of this equation.

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x is equal to 16.

217
00:09:49,580 --> 00:09:54,070
So the solution is 16 comma minus 3. x and y.

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00:09:54,070 --> 00:09:55,520
And that is choice D.

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00:09:55,519 --> 00:09:58,689


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All right, problem 37.

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Marcy has a total of 100 dimes and quarters.

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If the total value of the coins is $14.05, how many

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00:10:14,190 --> 00:10:15,780
quarters does she have?

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All right, so let's say that d is a number of dimes and q is

225
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the number of quarters.

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00:10:21,000 --> 00:10:24,289
So if you take the number of dimes plus the number of

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quarters she has 100 coins.

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That's this piece of information right there.

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And then the total value of the coins.

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It's going to be 0.10 times the number of dimes plus 0.25

231
00:10:41,179 --> 00:10:43,109
times the number of quarters.

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And they tell us that that is equal to $14.05.

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And that's this piece of information.

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The total value of the coins is $14.05.

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And they say, well, how many quarters does she have?

236
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So we just have to solve for q.

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00:10:59,639 --> 00:11:01,370
So let's do that.

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00:11:01,370 --> 00:11:04,269
So if we want to cancel out the d's, what we could do is

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00:11:04,269 --> 00:11:06,639
we can multiply this top equation by

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let's say, minus 0.1.

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And I'm doing that so it cancels out with

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this d right here.

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Let me do it in a different color.

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00:11:14,850 --> 00:11:20,820
So if I multiply that top equation times minus 0.1 I get

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00:11:20,820 --> 00:11:27,500
minus 0.1d-- I could write 1-0 if I want-- d.

246
00:11:27,500 --> 00:11:35,029
Minus 0.10q is equal to-- what's minus 1/10 of 100?

247
00:11:35,029 --> 00:11:38,649
Well that's minus 10, right?

248
00:11:38,649 --> 00:11:42,090
100 times 0.1 is 10 and we're doing a minus 0.1.

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00:11:42,090 --> 00:11:43,930
All right, now we can add these two equations.

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251
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0.1d minus 0.1d, those cancel out.

252
00:11:50,210 --> 00:11:55,509
0.25q minus 0.1q, that's equal to-- let me switch colors.

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That's equal to 0.15q is equal to-- and

254
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what's 14.05 minus 10?

255
00:12:03,549 --> 00:12:07,229
That's equal to $4.05.

256
00:12:07,230 --> 00:12:09,220
Just to get rid of the decimals, we can multiply both

257
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sides of this equation by 100.

258
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So we'll get 15q is equal to 405.

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00:12:20,159 --> 00:12:20,600
So q.

260
00:12:20,600 --> 00:12:22,759
We divide both sides of this by 15.

261
00:12:22,759 --> 00:12:27,480
And so how many times does 15 go into 405?

262
00:12:27,480 --> 00:12:28,870
15 goes into 40, what?

263
00:12:28,870 --> 00:12:29,570
Two times.

264
00:12:29,570 --> 00:12:34,940
2 times 15 is 30.

265
00:12:34,940 --> 00:12:36,080
Get a 10.

266
00:12:36,080 --> 00:12:37,310
105.

267
00:12:37,309 --> 00:12:41,469
15 goes into 105 seven times I think.

268
00:12:41,470 --> 00:12:44,540
7 times 5 is 35.

269
00:12:44,539 --> 00:12:45,750
7 times 1 is 7.

270
00:12:45,750 --> 00:12:46,990
Plus 3 is 10.

271
00:12:46,990 --> 00:12:47,669
27.

272
00:12:47,669 --> 00:12:50,099
So q is equal to 27.

273
00:12:50,100 --> 00:12:53,570
So Marcy has 27 quarters.

274
00:12:53,570 --> 00:12:56,030
Anyway, see you in the next video.