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