Step 1) Solve the second equation for #y#:
#-3x + y = 18#
#-3x + color(red)(3x) + y = 18 + color(red)(3x)#
#0 + y = 18 + 3x#
#y = 3x + 18#
Step 2) Substitute #3x + 18# for #y# in the first equation and solve for #x#:
#4x - 12y = -3#
#4x - 12(3x + 18) = -3#
#4x - 36x - 216 = -3#
#-32x - 216 = -3#
#-32x - 216 + color(red)(216) = -3+ color(red)(216)#
#-32x - 0 = 213#
#-32x = 213#
#(-32x)/color(red)(-32) = 213/color(red)(-32)#
#(color(red)(cancel(color(black)(-32)))x)/cancel(color(red)(-32)) = -6.65625#
#x = -6.65625#
Step 3) Substitute #-6.65625# for #x# into the solution for #y# in the second equation in Step 1 and calculate #y#:
#y = 3x + 18#
#y = (3 xx -6.65625) + 18#
#y = -19.96875 + 18#
#y = -1.96875#
The solution is: #x = -6.65625# and #y = -1.96875#
