Step 1) Solve the second equation for #x#:
#x - 5y = -9#
#x - 5y + color(red)(5y) = -9 + color(red)(5y)#
#x - 0 = -9 + 5y#
#x = -9 + 5y#
Step 2) Substitute #(-9 + 5y)# for #x# in the first equation and solve for #y#:
#6x + 2y = -4# becomes:
#6(-9 + 5y) + 2y = -4#
#(6 xx -9) + (6 xx 5y) + 2y = -4#
#-54 + 30y + 2y = -4#
#-54 + (30 + 2)y = -4#
#-54 + 32y = -4#
#-54 + color(red)(54) + 32y = -4 + color(red)(54)#
#0 + 32y = 50#
#32y = 50#
#(32y)/color(red)(32) = 50/color(red)(32)#
#(color(red)(cancel(color(black)(32)))y)/cancel(color(red)(32)) = 25/16#
#y = 25/16#
Step 3) Substitute #25/16# for #y# in the solution to the second equation at the end of Step 1 and calculate #x#:
#x = -9 + 5y# becomes:
#x = -9 + (5 xx 25/16)#
#x = (16/16 xx -9) + 125/16#
#x = -144/16 + 125/16#
#x = -19/16#
The Solution Is:
#x = -19/16# and #y = 25/16#
Or
#(-19/16, 25/16)#
