Step 1) Solve the first equation for xx:
3x +3y = -93x+3y=−9
(3x +3y)/color(red)(3) = -9/color(red)(3)3x+3y3=−93
(3x)/color(red)(3) +(3y)/color(red)(3) = -33x3+3y3=−3
x + y = -3x+y=−3
x + y - color(red)(y) = -3 - color(red)(y)x+y−y=−3−y
x + 0 = -3 - yx+0=−3−y
x = -3 - yx=−3−y
Step 2) Substitute (-3 - y)(−3−y) for xx in the second equation and solve for yy:
6x + 2y = 26x+2y=2 becomes:
6(-3 - y) + 2y = 26(−3−y)+2y=2
(6 xx -3) - (6 xx y) + 2y = 2(6×−3)−(6×y)+2y=2
-18 - 6y + 2y = 2−18−6y+2y=2
-18 + (-6 + 2)y = 2−18+(−6+2)y=2
-18 + (-4)y = 2−18+(−4)y=2
-18 - 4y = 2−18−4y=2
-18 + color(red)(18) - 4y = 2 + color(red)(18)−18+18−4y=2+18
0 - 4y = 200−4y=20
-4y = 20−4y=20
(-4y)/color(red)(-4) = 20/color(red)(-4)−4y−4=20−4
(color(red)(cancel(color(black)(-4)))y)/cancel(color(red)(-4)) = -5
y = -5
Step 3) Substitute -5 for y in the solution to the first equation at the end of Step 1 and calculate x:
x = -3 - y becomes:
x = -3 - (-5)
x = -3 + 5
x = 2
The Solution Is:
x = 2 and y = -5
Or
(2, -5)
