Question

How do you solve `x-2y=4` and `-x+6y=12`?

Answer 1

`color(green)(x = 12`
`color(green)(y = 4`

Explanation:

`x-2y=4` -----(1)
`-x+6y=12` ------(2)

The question is asking us the find the values of x and y which satisfy both these equations

To find the value of `x`, we just need to eliminate `y`

We can do that by adding the two equations. We get:

`(x - 2y) + (-x + 6y) = 4+12`

`->cancel(x) - 2y - cancel(x) + 6y = 16`

`4y = 16`

`color(green)(y = 4`

To get the value of `x`, we can easily substitute this value of `y` in any of the two equations

Substituting it in the first equation, we get

`x - 2(4) = 4`

`->x - 8 = 4`

Transposing `8` to the other side, we get

`-> x = 4 + 8`

`color(green)(x = 12`