What is the solution to the system of equations: #6=-4x+y, -5x-y=21#?

1 Answer
Nov 23, 2016

Answer:

#x=-3# and #y=-6#

Explanation:

  1. #6=-4x+y#
  2. #-5x-y=21#

From the first equation we can determine a value for #y#.

#6=-4x+y#

Add #4x# to both sides.

#4x+6=y#

In the second equation, substitute #y# with #color(red)((4x+6))#.

#-5x-color(red)((4x+6))=21#

Open the brackets and simplify. The multiplication of a negative and a positive results in a negative.

#-5x-color(red)(4x-6)=21#

#-9x-6=21#

Add #6# to both sides.

#-9x=27#

Divide both sides by #9#.

#-x=3# or #x=-3#

In the first equation, substitute #x# with #-3#.

#6=-4(-3)+y#

Open the brackets. The multiplication of two negatives results in a positive.

#6=12+y#

Subtract #12# from both sides.

#-6=y# or #y=-6#