Question

How do you solve `x+4y=-1, -3x-14=y` by substitution?

1. List item

Answer 1

`x=-5` and `y=1`

Explanation:

`x+4y=-1`
`-3x-14=y`

From the second equation, we know the value of `y` as `color(red)((-3x-14))`. So in the first equation, substitute `y` with `color(red)((-3x-14))`.

`x+4y=-1`

`x+ 4color(red)((-3x-14))=-1`

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

`x-12x-56=-1`

`-11x-56=-1`

Add `56` to both sides.

`-11x=55`

Divide both sides by `11`.

`-x=5` or `x=-5`

In the first equation, substitute `x` with `color(blue)(-5)`.

`x+4y=-1`

`color(blue)(-5)+4y=-1`

Add `5` to both sides.

`4y=4`

Divide both sides by `4`.

`y=1`