How do you solve #8x-5y= -46# and #8x+ 86=y# using substitution?

1 Answer
May 29, 2018

Answer:

#x=-12#
#y=-10#

Explanation:

You have the value for y. This makes substitution easier.
#y = 8x + 86#. Plug that into the other equation #8x-5y = -46#
#8x - 5 (8x + 86) = -46#
Distribute terms and combine like terms.
#8x - 40x - 430 = -46#
We are left with #-32x - 430 = -46#
Solve for x by isolating it.
Add 430 to both sides
#-32x = 384#
Divide both sides by -32
#x = -12#

Oops. Forgot to solve for y.
Plug the value in for x into one of the equations.
#8(-12) - 5y = -46#
Simplify.
#-96 - 5y = -46#
Add 96 to both sides.
#-5y = 50#
Divide both sides by -5
#y = -10#

Now, check your answers. Plug -12 for x and -10 for y in the second equation.
#8(-12) + 86 = -10#
Simplify
#-96 + 86 = -10#
#-10 = -10#