Step 1) Solve the second equation for xx:
x + 3y = -8x+3y=−8
x + 3y - color(red)(3y) = -8 - color(red)(3y)x+3y−3y=−8−3y
x + 0 = -8 - 3yx+0=−8−3y
x = -8 - 3yx=−8−3y
Step 2) Substitute -8 - 3y−8−3y for xx in the first equation and solve for yy:
2x + y = 62x+y=6 becomes:
2(-8 - 3y) + y = 62(−8−3y)+y=6
-16 - 6y + y = 6−16−6y+y=6
-16 - 5y = 6−16−5y=6
color(red)(16) - 16 - 5y = color(red)(16) + 616−16−5y=16+6
0 - 5y = 220−5y=22
-5y = 22−5y=22
(-5y)/color(red)(-5) = 22/color(red)(-5)−5y−5=22−5
(color(red)(cancel(color(black)(-5)))y)/cancel(color(red)(-5)) = -22/5
y = -22/5
Step 3) Substitute -22/5 for y in the solution to the second equation at the end of Step 1 and calculate x:
x = -8 - 3y becomes:
x = -8 - (3 xx -22/5)
x = -8 - (-66/5)
x = -8 + 66/5
x = (5/5 xx -8) + 66/5
x = -40/5 + 66/5
x = 26/5
The solution is: x = 26/5 and y = -22/5 or (26/5, -22/5)
