How do you solve using elimination of #2x - 3y = 12# and #3x + 5y = -1#?

1 Answer
Jun 11, 2018

Answer:

#x=3#
#y=-2#

Explanation:

On paper you should line the equations up, one below the other:

#2x-3y=12#
#3x+5y=-1#

In elimination, you have to find the least common multiple between one of the variables. I prefer to eliminate #x# and solve for #y# first and so the least common multiple between #2x# and #3x# is #6x#.

You’ll have to multiply #2x-3y=12# by #3# and
#3x+5y=-1# by #2#

#6x-9y=-36#
#6x+10y=-2#

Now you have to combine the equations by subtracting the bottom equation from the top:

#-19y=38#
Notice that we added #2# to #36# because if you try to subtract a negative, the negative turns positive.

Now to isolate #y#, divide both sides by #-19#

#y=-2#

Now that we found #y#, let’s subtitute it into either equation to find #x#. I’ll choose the top equation:

#2x-3(-2)=12#
#2x+6=12#

Now, we subtract #6# from both sides in an attempt to isolate #x#.

#2x=6#

Divide both sides by #2#

#x=3#

And there you go!

#y=-2# and #x=3#

Hope this helps!