The tables represent two linear functions in a system.

label Algebra
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Jun 24th, 2015

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We set up 2 equations based on the tables

Using the y intercept where x = 0 , we get

y = mx + 10 for the first equation (since the table tells us that y = 10 when x = 0)

and

y = mx + 2

Now plug in values for the first equation based on the given table

For x = 2, y = 2

then,

2 = 2m + 10

2m = -8

m = -4

So the first equation must be

y = -4x + 10

Now plug in values for the second equation based on its table

For x = 2, y = -4

then,

-4 = 2m + 2

2m = - 6

m = -3

So the second equation must be

y = -3x + 2

Set both equations equal to each other to find the solution:

-4x + 10 = -3x + 2

x = 8

plug x into either equation

y = -3(8) + 2

y = -22

therefore the solution is

(8, -22)  the last choice

Please let me know if you need any clarification. I'm always happy to answer your questions.
Jun 24th, 2015

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