Step 1) Solve the first equation for xx:
x + 2y = 1x+2y=1
x + 2y - color(red)(2y) = 1 - color(red)(2y)x+2y−2y=1−2y
x + 0 = 1 - 2yx+0=1−2y
x = 1 - 2yx=1−2y
Step 2) Subsitute 1 - 2y1−2y for xx in the second equation and solve for yy:
-3x - 8y = -9−3x−8y=−9 becomes:
-3(1 - 2y) - 8y = -9−3(1−2y)−8y=−9
(-3 * 1) - (-3 * 2y) - 8y = -9(−3⋅1)−(−3⋅2y)−8y=−9
-3 - (-6y) - 8y = -9−3−(−6y)−8y=−9
-3 + 6y - 8y = -9−3+6y−8y=−9
-3 + (6 - 8)y = -9−3+(6−8)y=−9
-3 - 2y = -9−3−2y=−9
color(red)(3) - 3 - 2y = color(red)(3) - 93−3−2y=3−9
0 - 2y = -60−2y=−6
-2y = -6−2y=−6
(-2y)/color(red)(-2) = -6/color(red)(-2)−2y−2=−6−2
(color(red)(cancel(color(black)(-2)))y)/cancel(color(red)(-2)) = 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 = 1 - 2y becomes:
x = 1 - (2 * 3)
x = 1 - 6
x = -5
The solution is: x = -5 and y = 3 or (-5, 3)
