How do you solve 4x + 5y = 1 and 7y - 3x = 2?

1 Answer
Sep 21, 2015

Answer:

#x=-3/43#
#y=11/43#

Explanation:

There are two ways you can solve this: substitution or elimination. I'll go with substitution since I personally like it better.

Let's try looking for the value of #x# first. We'll first try to isolate #y# in the first equation.
#4x+5y=1#
#5y=1-4x#
#y=(1-4x)/5#

Now we will substitute this value of #y# to the second equation.
#7y-3x=2#
#7((1-4x)/5)-3x=2#
(We'll multiply both sides by 5 to remove the denominator)
#(5)[7((1-4x)/5)-3x]=(5)(2)#
#7(1-4x)-15x=10#
#7-28x-15x=10#
#7-43x=10#
#-43x=10-7#
#-43x=3#
#x=-3/43#

To solve for #y#, substitute the value of #x# we just got into either of the two equations.
#4x+5y=1#
#4(-3/43)+5y=1#
#-12/43+5y=1#
#5y=1+12/43#
#5y=43/43+12/43#
#5y=55/43#
#(1/5)5y=(1/5)55/43#
#y=11/43#