Step 1) Solve the first equation for #y#:
#-6x + y = -8#
#-6x + color(red)(6x) + y = -8 + color(red)(6x)#
#0 + y = -8 + 6x#
#y = -8 + 6x#
Step 2) Substitute #(-8 + 6x)# for #y# in the second equation and solve for #x#
#2x + 3y = 4# becomes:
#2x + 3(-8 + 6x) = 4#
#2x + (3 xx -8) + (3 xx 6x) = 4#
#2x - 24 + 18x = 4#
#2x + 18x - 24 = 4#
#(2 + 18)x - 24 = 4#
#20x - 24 = 4#
#20x - 24 + color(red)(24) = 4 + color(red)(24)#
#20x - 0 = 28#
#20x = 28#
#(20x)/color(red)(20) = 28/color(red)(20)#
#(color(red)(cancel(color(black)(20)))x)/cancel(color(red)(20)) = 7/5#
#x = 7/5#
Step 3) Substitute #7/5# for #x# in the solution to the first equation at the end of Step 1 and calculate #y#:
#y = -8 + 6x# becomes:
#y = -8 + (6 xx 7/5)#
#y = (5/5 xx -8) + 42/5#
#y = -40/5 + 42/5#
#y = 2/5#
The Solution Is:
#x = 7/5# and #y = 2/5#
Or
#(7/5, 2/5)#
