Answer: (4,3)
Rearrange the first equation so that only y is on the left side.
x + 2y = 10
Subtract x on both sides.
2y = -x + 10
Divide by 2 on both sides, to get y by itself.
y = -0.5x + 5
Rearrange the second equation so that only y is on the left side.
2x - y = 5
Subtract 2x on both sides.
-y = -2x +5
To get rid of the negative sign on front of y, divide both sides by -1.
y = 2x - 5
Now you have: y = -0.5x + 5 and y = 2x - 5. Because both equations are equal to y, you can set both of these two equations equal to each other in order to solve for x.
-0.5 x + 5 = 2x - 5
Add 0.5x to both sides.
5 = 2.5x -5
Add 5 to both sides.
10 = 2.5x
Divide both sides by 2.5.
x = 4
Now that you have the value of x (x=4), use one of the original equations and substitute the x for 4.
x + 2y = 10.
(4) + 2y = 10
Subtract 4 on both sides.
2y = 6
Divide by 3 on both sides.
y = 3
x=4 and y=3 can also be written in (x,y) form as (4,3).