Step 1) Solve the second equation for xx:
x + 2y = 2x+2y=2
x + 2y - 2y = 2 - 2yx+2y−2y=2−2y
x + 0 = 2 - 2yx+0=2−2y
x = 2 - 2yx=2−2y
Step 2) Substitute color(red)(2 - 2y)2−2y for xx in the first equation and solve for yy:
3(color(red)(2 - 2y)) + 4y = -43(2−2y)+4y=−4
6 - 6y + 4y = -46−6y+4y=−4
6 - 2y = -46−2y=−4
6 - 6 - 2y = -4 - 66−6−2y=−4−6
0 - 2y = -100−2y=−10
-2y = -10−2y=−10
(-2y)/color(red)(-2) = (-10)/color(red)(-2)−2y−2=−10−2
(color(red)(cancel(color(black)(-2)))y)/cancel(color(red)(-2)) = 5
y = 5
Step 3) Substitute color(red)(5) for y in the solution to the second equation at the end of Step 1 and calculate x:
x = 2 - (2 xx color(red)(5))
x = 2 - 10
x = -8
The solution is:
x = -8 and y = 5 or (-8, 5)
