Question

How do you solve the system of linear equations `5x - 4y = 7, 2y + 6x = 22`?

Answer 1

`x=3` and `y=2`.

Explanation:

`5x-4y=7`
`2y+6x=22`

From the second equation, we can determine a value for `4y`.

`2y+6x=22`

Multiply all terms by `2`.

`4y+12x=44`

Subtract `12x` from both sides.

`4y=44-12x`

In the first equation, replace `4y` with `color(red)((44-12x))`.

`5x-4y=7`

`5x-color(red)((44-12x))=7`

Open the brackets and simplify. The product of two negatives i a positive.

`5x-color(red)(44+12x)=7`

`17x-44=7`

Add `44` to both sides.

`17x=51`

Divide both sides by `17`.

`x=3`

In the second equation, substitute `x` with `3`.

`2y+6x=22`

`2y+(6xx3)=22`

`2y+18=22`

Subtract `18` from both sides.

`2y=4`

Divide both sides by `2`.

`y=2`