How do you solve the system of linear equations #x + 3y = 5# and #2x - y = 5#?

1 Answer
May 30, 2018

Answer:

#20/7 = x#, #5/7 = y#

Explanation:

#x+3y = 5#

#2x - y = 5#

If both equations equal #5#, we can set them equal to eachother

#x + 3y = 2x - y#

#4y = x#

Now we can substitute #4y# for #x# in one of the equations (let's pick the first one)

#4y + 3y = 5#

#7y = 5#

#y = 5/7#

Now, if #4y = x#, then #4 xx 5/7 = x# or #x = 20/7#

Now to check our work. Let's substitute #5/7# and #20/7# for #y# and #x# in the second equation. If we have the correct answers, our equation should still equal #5#.

#2(20/7) - 5/7#

#40/7 - 5/7#

#35/7#, which simplifies to #5#! So we were correct.