Question

How do you solve the system of equations `3x - 2y = 1` and `4y=7+3x`?

Answer 1

`x=3` and `y=4`

Explanation:

`3x-2y=1`
`4y=7+3x`

From the first equation, determine a temporary value for `3x`.

`3x-2y=1`

Add `2y` to both sides.

`3x=1+2y`

In the second equation, substitute `3x` with `color(red)((1+2y))`.

`4y=7+3x`

`4y=7+color(red)((1+2y))`

Open the brackets and simplify.

`4y=7+1+2y`

`4y=8+2y`

Subtract `2y` from both sides.

`2y=8`

Divide both sides by `@`.

`y=4`

In the first equation, substitute `y` with `color(blue)(4)`.

`3x-2y=1`

`3x-2(color(blue)(4))=1`

Open the brackets and simplify.

`3x-8=1`

Add `8` to both sides.

`3x=9`

Divide both sides by `3`.

`x=3`