How do you solve the system using the elimination method for 3x+y=4 and 6x+2y=8?

2 Answers
Jul 8, 2015

Answer:

Any value of #x# will satisfy the system of equations with #y=4-3x#.

Explanation:

Re-arrange the first equation to make #y# the subject:
#y=4-3x#

Substitute this for #y# in the second equation and solve for #x#:
#6x+2y=6x+2(4-3x)=8#

This eliminates #x# meaning there is no unique solution. Therefore any value of #x# will satisfy the system of equations as long as #y=4-3x#.

Jul 8, 2015

Answer:

You have #oo# solutions because the two equations represent two coincident lines!

Explanation:

These two equations are related and represent 2 coincident lines; the second equation is equal to the first multiplied by #2#!
The two equations have #oo# solutions (set of #x# and #y# values) in common.
You can see this by multiplying the first by #-2# and adding to the second:
#{-6x-2y=-8#
#{6x+28=8# adding you get:
#0=0# that it is always true!!!