Question

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

Answer 1

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`.

Answer 2

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!!!