Question

How do you solve the system of equations `-3x-4y=20` and `x-10y=16`?

Answer 1

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

Explanation:

Given system of equations

`-3x-4y=20\ ........(1)`

`x-10y=16\ ........(2)`

Multiplying (2) by `3` & adding to (1) as follows

`-3x-4y+3(x-10y)=20+3\cdot 16`

`-34y=68`

`y=-2`

setting `y=-2` in (1) we get

`x=\frac{-4y-20}{3}`

`=\frac{-4(-2)-20}{3}`

`=-4`

Answer 2

Express `x` as a function of `y` and replace in the second equation.

Explanation:

To get a very fast answer to your problem, just use one of the two equations to express `x` or `y`. In this case, let's do it with `x`.

So, we have the following system:

`1) \ -3x-4y=20`
`2) \ x-10y=16`

If we express `x` in `2)`, then we have:

`x=16+10y`

Then we replace `x` in `1)` with what we obtained with `2)` and we get:

`-3*(16+10y)-4y=20`

Then develop the brackets:

`-48-30y-4y=20`

Solve for `y`:

`-34y=68`

`y=-2`

Then replace `y` in `2)` by what you found:

`x-10*(-2)=16`

Solve for `x`:

`x=-4`

Finished!