Step 1) Solve the first equation for #x#:
#3x + 3y = 1#
#(3x + 3y)/color(red)(3) = 1/color(red)(3)#
#(3x)/color(red)(3) + (3y)/color(red)(3) = 1/3#
#x + y = 1/3#
#x + y - color(red)(y) = 1/3 - color(red)(y)#
#x + 0 = 1/3 - y#
#x = 1/3 - y#
Step 2) Substitute #(1/3 - y)# for #x# in the second equation and solve for #y#:
#-20x + 13y = -8# becomes:
#-20(1/3 - y) + 13y = -8#
#(-20 xx 1/3) + (-20 xx -y) + 13y = -8#
#-20/3 + 20y + 13y = -8#
#-20/3 + (20 + 13)y = -8#
#-20/3 + 33y = -8#
#-20/3 + color(red)(20/3) + 33y = -8 + color(red)(20/3)#
#0 + 33y = (3/3 xx -8) + color(red)(20/3)#
#33y = -24/3 + color(red)(20/3)#
#33y = (-24 + color(red)(20))/3#
#33y = -4/3#
#33y xx 1/color(red)(33) = -4/3 xx 1/color(red)(33)#
#color(red)(cancel(color(black)(33)))y xx 1/cancel(color(red)(33)) = -4/99#
#y = -4/99#
Step 3) Substitute #-4/99# for #y# in the solution to the first equation at the end of Step 1 and calculate #x#:
#x = 1/3 - y# becomes:
#x = 1/3 - (-4/99)#
#x = (33/33 xx 1/3) + 4/99#
#x = 33/99 + 4/99#
#x = (33 + 4)/99#
#x = 37/99#
The Solution Is:
#x = 37/99# and #y = -4/99#
Or
#(37/99, -4/99)#
