How do you solve the following system: #2x – 4y = 8, 2x-3y=-13#?

1 Answer
Apr 13, 2018

Answer:

#x=-38#, #y=-21#

Explanation:

One of the easiest ways to solve this is by realizing that when you subtract the equations, the x's cancel and you can solve for y.
#2x-4y=8#
#-(2x-3y=-13)#

You end up with:
#-y=21#, or #y=-21#

Then just plug it back into one of the equations for y, like this:
#2x-4(-21)=8#
Solve for x,
#2x+84=8#
#2x=-76#
#x=-38#

You could also solve by substitution.
Start by solving one of the equations for x or y- let's solve the first one for x:
#2x-4y=8#
#2x=4y+8#
#x=2y+4#
This is the same as x, right? So we can replace this for x in the second equation:
#2(2y+4)-3y=-13#
We've gotten rid of the x's, so we can solve for y:
#4y+8-3y=-13#
#y=-21#

Now just plug this y value into one of the equations and solve for x:
#2x-4(-21)=8#
#2x+84=8#
#2x=-76#
#x=-38#