How do you solve the system #7x + 2y = 2# and #6x - 2y = 8#?

1 Answer
May 16, 2015

I notice that all the terms in the second equation are divisible by 2 and it will be easy to isolate #y#, so let's do that first.

#6x-2y=8#

Divide both sides by 2 to get

#3x-y=4#

Add #y# to both sides to get

#3x=4+y#

Subtract 8 from both sides to get

#y = 3x-4#

Now substitute this expression for #y# into the first equation...

#2 = 7x+2y#

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

#= 7x + 6x - 8#

#=13x - 8#

Add 8 to both sides to get

#13x=10#

Divide both sides by 13 to get

#x = 10/13#

#y = 3x-4 = (3xx10)/13-4#

#= 30/13-(4xx13)/13#

#= (30-52)/13#

#= -22/13#