Step 1) Solve the first equation for xx:
x - 9y = -2x−9y=−2
x - 9y + color(red)(9y) = -2 + color(red)(9y)x−9y+9y=−2+9y
x - 0 = -2 + 9yx−0=−2+9y
x = -2 + 9yx=−2+9y
Step 2) Substitute -2 + 9y−2+9y for xx in the second equation and solve for yy:
-2x + 5y = -9−2x+5y=−9 becomes:
-2(-2 + 9y) + 5y = -9−2(−2+9y)+5y=−9
(-2 * -2) + (-2 * 9y) + 5y = -9(−2⋅−2)+(−2⋅9y)+5y=−9
4 - 18y + 5y = -94−18y+5y=−9
4 + (-18 + 5)y = -94+(−18+5)y=−9
4 + (-13)y = -94+(−13)y=−9
4 - 13y = -94−13y=−9
-color(red)(4) + 4 - 13y = -color(red)(4) - 9−4+4−13y=−4−9
0 - 13y = -130−13y=−13
-13y = -13−13y=−13
(-13y)/color(red)(-13) = (-13)/color(red)(-13)−13y−13=−13−13
(color(red)(cancel(color(black)(-13)))y)/cancel(color(red)(-13)) = 1
y = 1
Step 3) Substitute 1 for y in the solution to the first equation at the end of Step 1 and calculate x:
x = -2 + 9y becomes:
x = -2 + (9 * 1)
x = -2 + 9
x = 7
The solution is: x = 7 and y = 1 or (7, 1)
