#8x + 5y = -3#
#-2x + y = 21#
Solving by Substitution
First, we're going to find an equation for the value of a variable to plug it into the other equation in the system. #-2x + y = 21# looks like it can easily be rearranged to get the equation for the value of #y#.
#-2x + y = 21#
Add #2x# to both sides to isolate for the equation for the value of #y#. You should now have:
#y = 2x + 21#
Now that you have the equation for the value of #y#, you can plug the terms #(2x + 21)# into where #y# would appear in the other equation of the system. So:
#8x + 5y = -3#
#8x + 5(2x + 21) = -3#
Distribute. What this means is that you'll be multiplying #2x# by #5# and #21# by #5#. So:
#5 * 2x = 10x#
#5 * 21 = 105#
Re-write the equation:
#8x + 10x + 105 = -3#
Combine like terms #(10x + 8 = 18x)#:
#18x + 105 = -3#
This is a two-step equation. Subtract #105# from both sides to cancel out #105# in order to get closer to finding the value of #x#.
#18x = -108#
Divide by #18# to isolate for #x#:
#-108/18 = x#
#-108/18 = -6#
#x = -6#
Plug the value of #x# back into the equation for the value of #y# to figure out #y#'s value:
#y = 2x + 21#
#y = 2(-6) + 21#
#y = -12 + 21#
#y = 9#
Plug these values back into the whole system to prove they're right:
#8x + 5y = -3#
#8(-6) + 5(9) = -3#
#-48 + 45 = -3#
#-3 = -3#
#-2x + y = 21#
#-2(-6) + 9 = 21#
#12 + 9 = 21#
#21 = 21#
These are the correct values.
