How do you solve #2x-y=-1# and #x+y=-5#?

1 Answer
Oct 2, 2016

Answer:

#(x,y) = (-2,-3)#

Explanation:

There are several ways to solve a system, so it's always best to choose the simplest method to avoid what we call "nuking mosquitos", i.e. using a complex solution for a simple problem

In this case, I think the easiest way is to sum the two equations: adding the left and right sides, we have

#2x-y+x+y = -1-5#

and thus

#3x=-6#

This should make clear why I chose to sum the two equations: we cancel #y# out, and can easily solve for #x#:

#3x=-6 \implies x = -2#

Once we know the value of #x#, we can obtain #y# by substitution:

#x+y=-2 \implies -2+y=-5 \implies y=-3#