Question

How do you solve `y=2x` and `6x+7y=20` using substitution?

Answer 1

Substitute the expression given for `y` from the first equation into the second equation;
solve the (modified) second equation for `x`;
then substitute the solution for `x` back into the first equation.

Explanation:

If `y=2x`
we can substitute `2x` in place of `y` in `6x+7y=20`

This gives us
`color(white)("XXX")6x+7(2x)=20`
which simplifies as
`color(white)("XXX")20x=20color(white)("XX")rarrcolor(white)("XX")x=1`

We can now substitute `1` for `x` back in `y=2x`
`color(white)("XXX")rarr y=2`

`(x,y)=color(green)(""(1,2))`