Step 1) Solve the first equation for #x#:
#x - 3y = -19#
#x - 3y + color(red)(3y) = -19 + color(red)(3y)#
#x - 0 = -19 + 3y#
#x = -19 + 3y#
Step 2) Substitute #(-19 + 3y)# for #x# in the second equation and solve for #y#:
#3x - 4y = -27# becomes:
#3(-19 + 3y) - 4y = -27#
#(3 xx -19) + (3 xx 3y) - 4y = -27#
#-57 + 9y - 4y = -27#
#-57 + (9 - 4)y = -27#
#-57 + 5y = -27#
#color(red)(57) - 57 + 5y = color(red)(57) - 27#
#0 + 5y = 30#
#5y = 30#
#(5y)/color(red)(5) = 30/color(red)(5)#
#(color(red)(cancel(color(black)(5)))y)/cancel(color(red)(5)) = 6#
#y = 6#
Step 3) Substitute #6# for #y# in the solution to the first equation at the end of Step 1 and calculate #x#:
#x = -19 + 3y# becomes:
#x = -19 + (3 xx 6)#
#x = -19 + 18#
#x = -1#
The Solution Is: #x = -1# and #y = 6# or #(-1, 6)#
