Question

How do you solve the following linear system `3x-7y=1, -3x+5y=1?`?

Answer 1

`x=-2` and `y=-1`

Explanation:

`3x-7y=1`
`-3x+5y=1`

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

`3x-7y=1`

Add `7y` to each side.

`3x=7y+1`

In the second equation, substitute `3x` with `color(red)((7y+1))`.

`-3x+5y=1`

`-color(red)((7y+1))+5y=1`

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

`-7y-1+5y=1`

`-2y-1=1`

Add `1` to both sides.

`-2y=2`

Divide both sides by `-2`.

`y=-1`

In the first equation, substitute `y` with `color(blue)(-1)`.

`3x-7y=1`

`3x-7color(blue)((-1))=1`

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

`3x+7=1`

Subtract `7` from each side.

`3x=-6`

Divide both sides by `3`.

`x=-2`