How do you solve #5x+y=15, 2x+y=12# using substitution?

1 Answer
Dec 10, 2016

Answer:

#x = 1# and #y = 10#

Explanation:

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

#5x - 5x + y = 15 - 5x#

#0 + y = 15 - 5x#

#y = 15 - 5x#

Step 2) Substitute #15 - 5x# for #y# in the second equation and solve for #x#:

#2x + (15 - 5x) = 12#

#2x + 15 - 5x = 12#

#2x + 15 - 15 - 5x = 12 - 15#

#2x - 5x + 0 = -3#

#(2 - 5)x = -3#

#-3x = -3#

#(-3x)/(-3) = (-3)/(-3)#

#(-3)/(-3)x = 1#

#1x = 1#

#x = 1#

Step 3) Substitute #1# for #x# in the solution to the first equation in Step 1) and calculate #y#:

#y = 15 - 5*1#

#y = 15 - 5#

#y = 10#