Step 1) Solve the first equation for #x#:
#x - 7y = 9#
#x - 7y + color(red)(7y) = 9 + color(red)(7y)#
#x - 0 = 9 + 7y#
#x = 9 + 7y#
Step 2) Substitute #9 + 7y# for #x# in the second equation and solve for #y#:
#7y = 3x + 1# becomes:
#7y = 3(9 + 7y) + 1#
#7y = (3 * 9) + (3 * 7y) + 1#
#7y = 27 + 21y + 1#
#7y = 28 + 21y#
#7y - color(red)(21y) = 28 + 21y - color(red)(21y)#
#(7 - color(red)(21))y = 28 + 0#
#-14y = 28#
#(-14y)/color(red)(-14) = 28/color(red)(-14)#
#(color(red)(cancel(color(black)(-14)))y)/cancel(color(red)(-14)) = -2#
#y = -2#
Step 3) Substitute #-2# for #y# in the solution to the first equation at the end of Step 1 and calculate #x#:
#x = 9 + 7y# becomes:
#x = 9 + (7 * -2)#
#x = 9 + (-14)#
#x = 9 - 14#
#x = -5#
The solution is: #x = -5# and #y = -2# or #(-5, -2)#
