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Is (3, -4) a solution to the equation 5x + 2y = 7?

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So they're saying,

3
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"Does x equal 3, y equal negative 4 satisfy this equation, or this relationship right here?"

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So one way to do it is to substitute x is equal to 3 and y is equal to negative 4 into this

5
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and see if 5 times x plus 2 times y does indeed equal 7

6
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So we have 5 times 3 plus 2 times -4

7
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This is equal to 15 plus -8, which does indeed equal 7.

8
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So it does satisfy the equations.

9
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So it is on the line; it is a solution.

10
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x = 3, y = -4 is a solution to this equation.

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So we've essentially answered our question: It is.

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Now another way to do it,

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and I'm not gonna go into details here,

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is you can actually graph the line.

15
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So maybe the line might look something like this,

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I'm not gonna do it in detail,

17
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and you see, if you have a very good drawing of it,

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you see whether the point lies on the line.

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If the point, when you graph the point, does lie on the line,

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it would be a solution.

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If the point somehow ends up not being on the line,

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then you'd know it isn't a solution.

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But to do this, you would have to have a very good drawing,

24
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so you could very precisely determine

25
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whether it's on the line.

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If you do the substitution method,

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if you just substitute the values into the equation

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to see if it comes out mathematically,

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this will always be exact.

30
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So this is all we really had to do,

31
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all we really have to do in this example.

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So it definitely is a solution to the equation