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)