Step 1) Solve the second equation for #y#:
#-3x + y = 19#
#color(red)(3x) - 3x + y = color(red)(3x) + 19#
#0 + y = 3x + 19#
#y = 3x + 19#
Step 2) Substitute #(3x + 19)# for #y# in the first equation and solve for #x#:
#-2x + 3y = 15# becomes:
#-2x + 3(3x + 19) = 15#
#-2x + (3 xx 3x) + (3 xx 19) = 15#
#-2x + 9x + 57 = 15#
#(-2 + 9)x + 57 = 15#
#7x + 57 = 15#
#7x + 57 - color(red)(57) = 15 - color(red)(57)#
#7x + 0 = -42#
#7x = -42#
#(7x)/color(red)(7) = -42/color(red)(7)#
#(color(red)(cancel(color(black)(7)))x)/cancel(color(red)(7)) = -6#
#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 = 3x + 19# becomes:
#y = (3 xx -6) + 19#
#y = -18 + 19#
#y = 1#
The solution is: #x = -6# and #y = 1# or #(-6, 1)#
