Step 1) Solve the first equation for #y#:
#2x + y = -6#
#-color(red)(2x) + 2x + y = -color(red)(2x) - 6#
#0 + y = -2x - 6#
#y = -2x - 6#
Step 2) Substitute #(-2x - 6)# for #y# in the second equation and solve for #x#:
#3x - y = -9# becomes:
#3x - (-2x - 6) = -9#
#3x + 2x + 6 = -9#
#(3 + 2)x + 6 = -9#
#5x + 6 = -9#
#5x + 6 - color(red)(6) = -9 - color(red)(6)#
#5x + 0 = -15#
#5x = -15#
#(5x)/color(red)(5) = -15/color(red)(5)#
#(color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5)) = -3#
#x = -3#
Step 3) Substitute #-3# for #x# in the solution to the first equation at the end of Step 1 and calculate #y#:
#y = -2x - 6# becomes:
#y = (-2 * -3) - 6#
#y = 6 - 6#
#y = 0#
The solution is: #x = -3# and #y = 0# or #(-3, 0)#
