Step 1) Solve the second equation for #y#:
#7x + 6y = -6#
#-color(red)(7x) + 7x + 6y = -color(red)(7x) - 6#
#0 + 6y = -color(red)(7x) - 6#
#6y = -color(red)(7x) - 6#
#(6y)/color(red)(6) = (-color(red)(7x) - 6)/color(red)(6)#
#(color(red)(cancel(color(black)(6)))y)/cancel(color(red)(6)) = (-7x)/6 - 6/color(red)(6)#
#y = -7/6x - 1#
Step 2) Substitute #-7/6x - 1# for #y# in the first equation and solve for #x#:
#-5x - 7y = -12# becomes:
#-5x - 7(-7/6x - 1) = -12#
#-5x + (7xx 7/6x) + (7xx 1) = -12#
#-5x + 49/6x + 7 = -12#
#(6/6 xx -5)x + 49/6x + 7 - color(red)(7) = -12 - color(red)(7)#
#-30/6x + 49/6x + 0 = -19#
#19/6x = -19#
#color(red)(6)/color(blue)(19) xx 19/6x = color(red)(6)/color(blue)(19) xx -19#
#cancel(color(red)(6))/cancel(color(blue)(19)) xx color(blue)(cancel(color(black)(19)))/color(red)(cancel(color(black)(6)))x = color(red)(6)/cancel(color(blue)(19)) xx -color(blue)(cancel(color(black)(19)))#
#x = -6#
Step 3) Substitute #-6# for #x# in the solution to the second equation at the end of Step 1 and calculate #y#:
#y = -7/6x - 1# becomes:
#y = (-7/6 xx -6) - 1#
#y = (-7/color(red)(cancel(color(black)(6))) xx -color(red)(cancel(color(black)(6)))) - 1#
#y = 7 - 1#
#y = 6#
The solution is: #x = -6# and #y = 6# or #(-6, 6)#
