Step 1) Solve the first equation for xx:
5x + 5y = -105x+5y=−10
(5x + 5y)/color(red)(5) = -10/color(red)(5)5x+5y5=−105
(5x)/color(red)(5) + (5y)/color(red)(5) = -25x5+5y5=−2
x + y = -2x+y=−2
x + y - color(red)(y) = -2 - color(red)(y)x+y−y=−2−y
x + 0 = -2 - yx+0=−2−y
x = -2 - yx=−2−y
Step 2) Substitute (-2 - y)(−2−y) for xx in the second equation and solve for yy:
-4x + 2y = -10−4x+2y=−10 becomes:
-4(-2 - y) + 2y = -10−4(−2−y)+2y=−10
(-4 xx -2) + (-4 xx -y) + 2y = -10(−4×−2)+(−4×−y)+2y=−10
8 + 4y + 2y = -108+4y+2y=−10
8 + (4 + 2)y = -108+(4+2)y=−10
8 + 6y = -108+6y=−10
8 - color(red)(8) + 6y = -10 - color(red)(8)8−8+6y=−10−8
0 + 6y = -180+6y=−18
6y = -186y=−18
(6y)/color(red)(6) = -18/color(red)(6)6y6=−186
(color(red)(cancel(color(black)(6)))y)/cancel(color(red)(6)) = -3
y = -3
Step 3) Substitute -3 for y in the solution to the first equation at the end of Step 1 and calculate x:
x = -2 - y becomes:
x = -2 - (-3)
x = -2 + 3
x = 1
The Solution Is:
x = 1 and y = -3
Or
(1, -3)
