Question

How do you solve the system of equations `x= 4y` and `3x - 12y = 3` by substitution?

Answer 1

The system has no solution.

Explanation:

Since we know that `x=4y` we can substitute that into the second equation everywhere we see an `x`.

Doing this gives us:

`3(4y)-12y=3`

which means that

`12y-12y=3`

but this gives us

`0=3`, which is not true.

That means the system has no solution.

Does this make sense? Well, if you look at the two given equations and rearrange them we get:

`y=(1/4)x` and `y=(1/4)x-1/4`.

Both equations are lines with a slope of `1/4` but with different `y`-intercepts, so the lines are parallel and do not intersect.