Question

How do you solve this system of equation: `3x - 5y = 10; 3x - 3y = - 6`?

Answer 1

`x=-10` and `y=-8`

Explanation:

`3x-5y=10`
`3x-3y=-6`

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

`3x-5y=10`

Add `5y` to each side.

`3x=10+5y`

In the second equation, substitute `3x` with `color(red)((10+5y))`.

`3x-3y=-6`

`color(red)((10+5y))-3y=-6`

Open the brackets and simplify.

`color(red)(10+5y)-3y=-6`

`10+2y=-6`

Subtract `10` from each side.

`2y=-16`

Divide each side by `2`.

`y=-8`

In the second equation, substitute `y` with `color(blue)(-8)`.

`3x-3y=-6`

`3x-3color(blue)((-8))=-6`

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

`3x+24=-6`

Subtract `24` from each side.

`3x=-30`

Divide each side by `3`.

`x=-10`