How do you solve the system of equations: #4x + 2y = 14# and #4x + 3y = 6#?

1 Answer
Nov 6, 2016

Answer:

#x = 15/2# and #y = -8#

Explanation:

Step 1) First solve the second equation for #y# while keeping both sides of the equation balanced:

#4x + 2y = 14#

#4x + 2y - 4x = 14 - 4x#

#2y = 14 - 4x#

#(2y)/2 = (14 - 4x)/2#

#y = 7 - 2x#

Step 2) Substitute #7 - 2x# for #y# in the first equation and solve for #x# while keeping both sides of the equation balanced:

4x + 3(7 - 2x) = 6#

#4x + 21 - 2x = 6#

#2x + 21 = 6#

#2x + 21 - 21 = 6 - 21#

#2x = -15#

#(2x)/2 = 15/2#

#x = 15/2#

Step 3) Substitute #15/2# for #x# in the solution for Step 1 to find #y#:

#y = 7 - 2(15/2)#

#y = 7 - 15#

#y = -8#