Step 1) Solve the second equation for xx:
x - 2y = -5x−2y=−5
x - 2y + color(red)(2y) = -5 + color(red)(2y)x−2y+2y=−5+2y
x - 0 = -5 + 2yx−0=−5+2y
x = -5 + 2yx=−5+2y
Step 2) Substitute (-5 + 2y)(−5+2y) for xx in the first equation and solve for yy:
2x - 9y = 52x−9y=5 becomes:
2(-5 + 2y) - 9y = 52(−5+2y)−9y=5
(2 * -5) + (2 * 2y) - 9y = 5(2⋅−5)+(2⋅2y)−9y=5
-10 + 4y - 9y = 5−10+4y−9y=5
-10 + (4 - 9)y = 5−10+(4−9)y=5
-10 + (-5)y = 5−10+(−5)y=5
-10 - 5y = 5−10−5y=5
color(red)(10) - 10 - 5y = color(red)(10) + 510−10−5y=10+5
0 - 5y = 150−5y=15
-5y = 15−5y=15
(-5y)/color(red)(-5) = 15/color(red)(-5)−5y−5=15−5
(color(red)(cancel(color(black)(-5)))y)/cancel(color(red)(-5)) = -3
y = -3
Step 3) Substitute -3 for y in the solution to the second equation at the end of Step 1 and calculate x:
x = -5 + 2y becomes:
x = -5 + (2 * -3)
x = -5 + (-6)
x = -11
The solution is: x = -11 and y = -3 or (-11, -3)
