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Solve the following system of linear equations using elimination. x+2y=5 5x-y= 3

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We are asked to use the elimination methos to solve the following system of linear equations:

x + 2 y = 5

5 x - y = 3

Since we notice that the terms in y are one positive in the first equation and the other negative in the second equation, we use this to try to get the second equation to have a y term that perfectly cancels the term in y of the other equation. In order to accomplish such, we multiply by 2 on both sides of the second equation:

2 ( 5 x - y) = 2 ( 3 )

10 x - 2 y = 6

now we combine term by term both equations:

x + 2 y = 5

10 x - 2 y = 6

___________

11 x + 0 = 11

11 x = 11

divide both sides by 11 to isolate x completely

x = 11 / 11

x = 1

Now we use this result in any of the original equations to find the value of the other variable (y) :

x + 2 y = 5

1 + 2 y = 5

subtract 1 from both sides

2 y = 5 - 1

2 y = 4

divide both sides by 2 to isolate y completely

y = 4 / 2

y = 2

Then our answer is: x = 1, and y = 2 which makes the coordinate pair ( 1, 2)

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