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

1 Answer
Mar 2, 2017

Answer:

#x=-11/17# and #y=1/17#

Explanation:

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

From the second equation, we can determine a temporary value for #y#.

#3x-y=-2#

Add #y# to each side.

#3x=y-2#

Add #2# to each side.

#3x+2=y#

In the first equation, substitute #y# with #color(red)((3x+2))#.

#-5x-4y=3#

#-5x-4color(red)((3x+2))=3#

Open the brackets ad simplify. The product of a negative and a positive is a negative.

#-5x-12x-8=3#

#-17x-8=3#

Add #8# to each side.

#-17x=11#

Divide both sides by #-17#.

#x=-11/17#

In the second equation, substitute #x# with #color(blue)((-11/17))#.

#3x-y=-2#

#3color(blue)((-11/17))-y=-2#

Open the brackets and simplify. The product of a positive and a negative is a negative.

#-33/17-y=-2#

Add #y# to each side.

#-33/17=y-2#

Add #2# to each side.

#-33/17+2=y#

#-33/17+(2xx17/17)=y#

#-33/17+34/17=y#

#(-33+34)/17=y#

#1/17=y#