Step 1) Solve the first equation for #y#:
#12x - 6y = -6#
#(12x - 6y)/color(red)(-6) = (-6)/color(red)(-6)#
#(12x)/color(red)(-6) - (6y)/color(red)(-6) = 1#
#-2x + y = 1#
#color(red)(2x) - 2x + y = color(red)(2x) + 1#
#0 + y = 2x + 1#
#y = 2x + 1#
Step 2) Substitute #2x + 1# for #y# in the second equation and solve for #x#:
#-6x + 2y = 8# becomes:
#-6x + 2(2x + 1) = 8#
#-6x + (2 * 2x) + (2 * 1) = 8#
#-6x + 4x + 2 = 8#
#-2x + 2 = 8#
#-2x + 2 - color(red)(2) = 8 - color(red)(2)#
#-2x + 0 = 6#
#-2x = 6#
#(-2x)/color(red)(-2) = 6/color(red)(-2)#
#(color(red)(cancel(color(black)(-2)))x)/cancel(color(red)(-2)) = -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 + 1# becomes:
#y = (2 * -3) + 1#
#y = -6 + 1#
#y = -5#
The solution is: #x = -3# and #y = -5# or #(-3, -5)#
