Step 1) Solve the first equation for #x#:
#x + 2y = 5#
#x + 2y - color(red)(2y) = 5 - color(red)(2y)#
#x + 0 = 5 - 2y#
#x = 5 - 2y#
Step 2) Substitute #(5 - 2y)# for #x# in the second equation and solve for #y#:
#-4x + y = -3# becomes:
#-4(5 - 2y) + y = -3#
#(-4 xx 5) - (-4 xx 2y) + y = -3#
#-20 - (-8y) + y = -3#
#-20 + 8y + y = -3#
#-20 + 8y + 1y = -3#
#-20 + (8 + 1)y = -3#
#-20 + 9y = -3#
#-20 + color(red)(20) + 9y = -3 + color(red)(20)#
#0 + 9y = 17#
#9y = 17#
#(9y)/color(red)(9) = 17/color(red)(9)#
#(color(red)(cancel(color(black)(9)))y)/cancel(color(red)(9)) = 17/9#
#y = 17/9#
Step 3) Substitute #17/9# for #y# in the solution to the first equation at the end of Step 1 and calculate #x#:
#x = 5 - 2y# becomes:
#x = 5 - (2 xx 17/9)#
#x = 5 - 34/9#
#x = (9/9 xx 5) - 34/9#
#x = 45/9 - 34/9#
#x = (45 - 34)/9#
#x = 11/9#
The Solution Is:
#x = 11/9# and #y = 17/9#
Or
#(11/9, 17/9)#
