Question

How do you solve the system `5x - y = - 14 + 2x + y` and `7x + 9y + 4 = 3x + 8y`?

Answer 1

`x=-2` and `y=4`

Explanation:

First simplify both equations:
`5x-y=-14+2x+y`

Subtract `2x` and `y` from both sides.

`3x-2y=-14`

`color(red)(7x+9y+4=3x+8y)`

Subtract `3x` and `8y` from both sides.

`color(red)(4x+y+4=0)`

Subtract `4` from each side.

`color(red)(4x+y=-4)`

So now we have two simplified equations:
`3x-2y=-14`
`color(red)(4x+y=-4)`

Using the second equation, determine a value for `y`.

`color(red)(4x+y=-4)`

Subtract `4x` from both sides.

`color(red)(y=-4-4x)`

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

`3x-2y=-14`

`3x-2color(red)((-4-4x))=-14`

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

`3x+color(red)(8+8x)=-14`

`11x+8=-14`

Subtract `8` from each side.

`11x=-22`

Divide both sides by `11`.

`x=-2`

In the second equation, substitute `x` with `color(blue)(-2)`.

`color(red)(4x+y=-4)`

`color(red)(4color(blue)((-2))+y=-4)`

Open the brackets and simplify. The product of a positive and a negative results in a negative.

`color(red)(-8+y=-4)`

Add `8` to both sides.

`color(red)(y=4)`