How do you solve #7x+2y=-31# and #-5x+y=27# using substitution?

1 Answer
Apr 23, 2017

Answer:

See the entire solution process below:

Explanation:

Step 1) Solve the second equation for #y#:

#-5x + y = 27#

#color(red)(5x) - 5x + y = color(red)(5x) + 27#

#0 + y = 5x + 27#

#y = 5x + 27#

Step 2) Substitute #5x + 27# for #y# in the first equation and solve for #x#:

#7x + 2y = -31# becomes:

#7x + 2(5x + 27) = -31#

#7x + (2 * 5x) + (2 * 27) = -31#

#7x + 10x + 54 = -31#

#17x + 54 = -31#

#17x + 54 - color(red)(54) = -31 - color(red)(54)#

#17x + 0 = -85#

#17x = -85#

#(17x)/color(red)(17) = -85/color(red)(17)#

#(color(red)(cancel(color(black)(17)))x)/cancel(color(red)(17)) = -5#

#x = -5#

Step 3) Substitute #-5# for #x# in the solution to the second equation at the end of Step 1 and calculate #y#:

#y = 5x + 27# becomes:

#y = (5 * -5) + 27#

#y = -25 + 27#

#y = 2#

The solution is: #x = -5# and #y = 2# or #(-5, 2)#