Question

How do you solve the system of equations `3x + 5y = 4` and `3x + 7y = 2`?

Answer 1

`x=3` and `y=-1`

Explanation:

`3x+5y=4`
`3x+7y=2`

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

`3x+5y=4`

Subtract `5y` from both sides.

`3x=4-5y`

In the second equation, substitute `3x` with `color(red)((4-5y))`.

`3x+7y=2`

`color(red)((4-5y))+7y=2`

Open the brackets and simplify.

`color(red)(4-5y)+7y=2`

`4+2y=2`

Subtract `4` from each side.

`2y=-2`

Divide both sides by `2`.

`y=-1`

In the first equation, substitute `y` with `-1`.

`3x+5y=4`

`3x+5(-1)=4`

Open brackets and simplify.

`3x-5=4`

Add `5` to both sides.

`3x=9`

Divide both sides by `3`.

`x=3`