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

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Answer 1 · 2016-12-12T13:54:38

#x = 1# and #y = 10#

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#

#-3x + 15 = 12#

#-3x + 15 - 15 = 12 - 15#

#-3x + 0 = -3#

#-3x = -3#

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

#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#