Step 1) Solve the first equation for #y#:
#3x + y = 5#
#3x - color(red)(3x) + y = -color(red)(3x) + 5#
#0 + y = -3x + 5#
#y = -3x + 5#
Step 2) Substitute #(-3x + 5)# for #y# in the second equation and solve for #x#:
#-8x - 4y = -12# becomes:
#-8x - 4(-3x + 5) = -12#
#-8x - (4 xx -3x) - (4 xx 5) = -12#
#-8x - (-12x) - 20 = -12#
#-8x + 12x - 20 = -12#
#(-8 + 12)x - 20 = -12#
#4x - 20 = -12#
#4x - 20 + color(red)(20) = -12 + color(red)(20)#
#4x - 0 = 8#
#4x = 8#
#(4x)/color(red)(4) = 8/color(red)(4)#
#(color(red)(cancel(color(black)(4)))x)/cancel(color(red)(4)) = 2#
#x = 2#
Step 3) Substitute #2# for #x# in the solution to the first equation at the end of Step 1 and calculate #y#:
#y = -3x + 5# becomes:
#y = (-3 xx 2) + 5#
#y = -6 + 5#
#y = -1#
The Solution Is:
#x = 2# and #y = -1#
Or
#(2, -1)#
