Step 1) Solve the first equation for #y#;
#3x = y + 1#
#3x - color(red)(1) = y + 1 - color(red)(1)#
#3x - 1 = y + 0#
#3x - 1 = y#
Step 2) Substitute #3x - 1# for #y# in the second equation and solve for #x#:
#4x - 5y = 18# becomes:
#4x - 5(3x - 1) = 18#
#4x - (5 xx 3x) + (5 xx 1) = 18#
#4x - 15x + 5 = 18#
#-11x + 5 = 18#
#-11x + 5 - color(red)(5) = 18 - color(red)(5)#
#-11x + 0 = 13#
#-11x = 13#
#(-11x)/color(red)(-11) = 13/color(red)(-11)#
#(color(red)(cancel(color(black)(-11)))x)/cancel(color(red)(-11)) = -13/11#
#x = -13/11#
Step 3) Substitute #13/11# for #x# in the solution to the first equation at the end of Step 1 and calculate #y#:
#3x - 1 = y# becomes:
#(3 x -13/11) - 1 = y#
#(3 x -13/11) - (1 xx 11/11) = y#
#-39/11 - 11/11 = y#
#-50/11 = y#
The solution is: #x = -13/11# and #y = -50/11# or #(-13/11, -50/11)#
