Step 1) Solve the second equation for xx:
x - 2y = 8x−2y=8
x - 2y + color(red)(2y) = 8 + color(red)(2y)x−2y+2y=8+2y
x - 0 = 8 + 2yx−0=8+2y
x = 8 + 2yx=8+2y
Step 2) Substitute 8 + 2y8+2y for xx in the first equation and solve for yy:
-4x - 14y = 28−4x−14y=28 becomes:
-4(8 + 2y) - 14y = 28−4(8+2y)−14y=28
(-4 xx 8) + (-4 xx 2y) - 14y = 28(−4×8)+(−4×2y)−14y=28
-32 - 8y - 14y = 28−32−8y−14y=28
-32 - 22y = 28−32−22y=28
color(red)(32) - 32 - 22y = color(red)(32) + 2832−32−22y=32+28
0 - 22y = 600−22y=60
-22y = 60−22y=60
(-22y)/color(red)(-22) = 60/color(red)(-22)−22y−22=60−22
(color(red)(cancel(color(black)(-22)))y)/cancel(color(red)(-22)) = (2 xx 30)/color(red)(2 xx -11)
y = (color(red)(cancel(color(black)(2))) xx 30)/color(red)(cancel(2) xx -11)
y = -30/11
Step 3) Substitute -30/11 for y in the solution to the second equation at the end of Step 1 and calculate x:
x = 8 + 2y becomes:
x = 8 + (2 xx -30/11)
x = (11/11 xx 8) - 60/11
x = 88/11 - 60/11
x = (88 - 60)/11
x = 28/11
The solution is: x = 28/11 and y = -30/11 or (28/11, -30/11)
