Step 1) Solve the first equation for xx:
x + 5y = -3x+5y=−3
x + 5y - color(red)(5y) = -3 - color(red)(5y)x+5y−5y=−3−5y
x + 0 = -3 - 5yx+0=−3−5y
x = -3 - 5yx=−3−5y
Step 2) Substitute -3 - 5y−3−5y for xx in the second equation and solve for yy:
3x - 2y = 83x−2y=8 becomes:
3(-3 - 5y) - 2y = 83(−3−5y)−2y=8
(3 xx -3) - (3 xx 5y) - 2y = 8(3×−3)−(3×5y)−2y=8
-9 - 15y - 2y = 8−9−15y−2y=8
-9 - 17y = 8−9−17y=8
color(red)(9) - 9 - 17y = color(red)(9) + 89−9−17y=9+8
0 - 17y = 170−17y=17
-17y = 17−17y=17
(-17y)/color(red)(-17) = 17/color(red)(-17)−17y−17=17−17
(color(red)(cancel(color(black)(-17)))y)/cancel(color(red)(-17)) = -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 = -3 - 5y becomes:
x = -3 - (5 xx -1)
x = -3 - (-5)
x = -3 + 5
x = 2
The solution is: x = 2 and y = -1 or (2, -1)
