How do you solve the system -2x + 2y= -5 and x + y= -5?

1 Answer
Mar 18, 2018

Answer:

#x = -5/4#, #" "y = -15/4#

Explanation:

Eq1: #-2x + 2y = -5#
Eq2: #x+y=-5#

We need to find one of the variables. Since Eq2 already has variables with coefficients of #1#, let's start there. Let's solve for #x# in Eq2:

Eq3: #x = -y-5#

Now we can use Eq3 by substituting it into Eq1. We cannot substitute into Eq2, as we have already used this equation to derive a result!

Eq3 -> Eq1:
#-2(-y-5)+2y=-5#
#=>2y+10+2y=-5#
#=>4y + 10 = -5#
#=>4y = -15#
#=> color(blue)(y = -15/4)#

We now have a value for #y#. We have both Eq1 and Eq2 that must hold. We can use whichever one, as both will give the same results. Let's just substitute into Eq2 for convenience:

#x+(color(blue)(-15/4))=-5#
# => color(orange)(x = -5/4)#

Now we have values for both #x# and #y#:
#x = -5/4#,#" " y = -15/4#