Question

How do you solve the system of equations `y+2x=3` and `-y+4=-x`?

Answer 1

`x=-1/3` and `y=11/3` or `3 2/3`

Explanation:

`y+2x=3`
`-y+4=-x`

In the first equation, we can determine a value for `y`.

`y+2x=3`

Subtract `2x` from both sides.

`y=3-2x`

In the second equation, substitute `y` with `color(red)((3-2x))`.

`-color(red)((3-2x))+4=-x`

Open the brackets and simplify. The product of two negatives is a positive, and that of a negative and positive is a negative.

`-3+2x+4=-x`

`2x+1=-x`

Add `x` to both sides.

`3x+1=0`

Subtract `1` from both sides.

`3x=-1`

Divide both sides by `3`.

`x=-1/3`

In the first equation, substitute `x` with `-1/3`.

`y+2x=3`

`y+2(-1/3)=3`

Open the brackets and simplify.

`y-2/3=3`

Add `2/3` to both sides.

`y=3+2/3`

`y=3 2/3` or `y=11/3`