How do you solve x+2y=5 and 2x-3y=-4?

1 Answer
Nov 4, 2015

Answer:

#x = 1#
#y = 2#

Explanation:

Ok. So prefer the elimination method, but you can do this with substitution as well.

First put the equations on top of each other

#x +2y= 5#
#2x-3y=-4#

Then find the variable that would be easiest to cancel out. I think it's #x# because you only have to modify one of the equations. Let's multiply the first equation by -2. This will allow us to cancel out the two #x#'s in the equations.

#-2x - 4y = -10#
#2x - 3y = -4#

Now let's add the two equations together!

#0x-7y = -14#

or just

#-7y = -14#

Now we simply divide by -7 to get #y#

#y = 2#

But wait! We're not done!

Plug #y# back into one of two equations to get #x#. I'll use the first equation again.

#x + 2(2) = 5#

which simplifies to

#x + 4 = 5#

So we subtract 4 from both sides, and get

#x = 1#

Hope this helps!