Step 1) Solve the first equation for #x#:
#3x +3y = -9#
#(3x +3y)/color(red)(3) = -9/color(red)(3)#
#(3x)/color(red)(3) +(3y)/color(red)(3) = -3#
#x + y = -3#
#x + y - color(red)(y) = -3 - color(red)(y)#
#x + 0 = -3 - y#
#x = -3 - y#
Step 2) Substitute #(-3 - y)# for #x# in the second equation and solve for #y#:
#6x + 2y = 2# becomes:
#6(-3 - y) + 2y = 2#
#(6 xx -3) - (6 xx y) + 2y = 2#
#-18 - 6y + 2y = 2#
#-18 + (-6 + 2)y = 2#
#-18 + (-4)y = 2#
#-18 - 4y = 2#
#-18 + color(red)(18) - 4y = 2 + color(red)(18)#
#0 - 4y = 20#
#-4y = 20#
#(-4y)/color(red)(-4) = 20/color(red)(-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)#
