Step 1) Solve each equation for x:
x + 2y = -2
x + 2y - color(red)(2y) = -2 - color(red)(2y)
x + 0 = -2 - 2y
x = -2 - 2y
x - 3y = -12
x - 3y + color(red)(3y) = -12 + color(red)(3y)
x - 0 = -12 + 3y
x = -12 + 3y
Step 2) Because the left side of both equations are the same we can equate the right sides and solve for y:
-2 - 2y = -12 + 3y
-2 + color(blue)(12) - 2y + color(red)(2y) = -12 + color(blue)(12) + 3y + color(red)(2y)
10 - 0 = 0 + (3 + color(red)(2))y
10 = 5y
10/color(red)(5) = (5y)/color(red)(5)
2 = (color(red)(cancel(color(black)(5)))y)/cancel(color(red)(5))
2 = y
y = 2
Step 3) Substitute 2 for y in the solutions to either of the equations in Step 1 and calculate x:
x = -12 + 3y becomes:
x = -12 + (3 xx 2)
x = -12 + 6
x = -6
The Solution Is:
x = -6 and y = 2
Or
(-6, 2)
