Question

How do you solve the system of equations `x- y = 1` and `6x + 5y = - 49`?

Answer 1

`x=-4` and `y=-5`

Explanation:

`x-y=1`
`6x+5y=-49`

From the first equation, we derive a value for `x`.

`x-y=1`

Add `y` to each side.

`x-y+y=1+y`

`x=1+y`

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

`6x+5y=-49`

`6color(blue)((1+y))+5y=-49`

Open the brackets and simplify.

`6+6y+5y=-49`

`6+11y=-49`

Subtract `6` from each side.

`6-6+11y=-49-6`

`11y=-55`

Divide both sides by `11`.

`(11y)/11=-55/11`

`(1cancel11y)/(1cancel11)=-(5cancel55)/(1cancel11)`

`y=-5`

In the first equation, substitute `y` with `color(red)(-5)`.

`x-y=1`

`x-(color(red)(-5))=1`

Open the brackets and simplify.

`x+5=1`

Subtract `5` from each side.

`x+5-5=1-5`

`x=-4`