How do you solve the following system?: #-3x -2y =5, -4x +7y = -3#

1 Answer
Dec 23, 2015

Answer:

#x=29/13# and #y=-47/13#

Explanation:

To solve this question there are a number of ways, the most basic being rearrangement and substitution.
To start off you would rearrange the top equation to get y by itself, to do this you would follow these steps
#-3x+3x-2y=5+3x#
Which gives the answer
#-2y=5+3x#
Y isn't by itself yet so you would then:
#(-2y)/-2=(5+3x)/-2#
Giving the answer
#y=-(5+3x)/2#

Now you must substitute this into the second equation, it would look like this:
#-4x+7[(-5+3x)/2]=-3#
You would then simplify to get:
#-8x-35+21x=-6#
Which then simplifies to:
#13x=32#
Therefore #x=29/13#

Then substitute the value of #x# into the equation where #y=-(5+3x)/2#
Which gives the answer:
#y=-47/13#