How do you find the solution of the system of equations #3x + 6y = 18# and #2x + 5y = 20#?

1 Answer
May 13, 2015

You just need to isolate #x# or #y# in one of the equations and then substitute it in the other.

Let's isolate #x# in the first:

#x# = #18/3 - 6y/3#

#x# = #6 - 2y#

Now, we replace this found #x# in the second:

#2(6 - 2y) + 5y = 20#

#12 - 4y + 5y = 20#

#12 + y = 20#

#y = 8#

Now, you just replace this #y = 8# in the isolated #x# above:

#x = 6 - 2(8)#

#x = 6 - 16 = -10#

(There are other possible ways, for example using matrixes or subtracting one equation from another, but I would only recommend that in case you have MORE than two variables. The resolution I posted appears to be the simplest).