How do you solve the following linear system #3x-7y=1, -3x+5y=1? #?

1 Answer
Mar 7, 2017

Answer:

#x=-2# and #y=-1#

Explanation:

#3x-7y=1#
#-3x+5y=1#

From the first equation, determine a temporary value for #3x#.

#3x-7y=1#

Add #7y# to each side.

#3x=7y+1#

In the second equation, substitute #3x# with #color(red)((7y+1))#.

#-3x+5y=1#

#-color(red)((7y+1))+5y=1#

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

#-7y-1+5y=1#

#-2y-1=1#

Add #1# to both sides.

#-2y=2#

Divide both sides by #-2#.

#y=-1#

In the first equation, substitute #y# with #color(blue)(-1)#.

#3x-7y=1#

#3x-7color(blue)((-1))=1#

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

#3x+7=1#

Subtract #7# from each side.

#3x=-6#

Divide both sides by #3#.

#x=-2#