How do you solve the system #x-4y=27# and #3x+y=-23# using substitution?

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Answer 1 · 2016-09-11T12:51:11

#x = - 5# and #y = - 8#

We have: #x - 4 y = 27# and #3 x + y = - 23#

Let's solve the first equation for #x#:

#=> x = 27 + 4 y#

Now, let's substitute this expression for #x# into the second equation:

#=> 3 (27 + 4 y) + y = - 23#

#=> 81 + 12 y + y = - 23#

#=> 13 y = - 104#

#=> y = - 8#

Now, let's substitute this value of #y# into the expression for #x#:

#=> x = 27 + 4 (- 8)#

#=> x = 27 - 32#

#=> x = - 5#

Therefore, the solutions to the system of equations are #x = - 5# and #y = - 8#.