Question

How do you solve the system of equations `-6x + 5y = - 5` and `10x - 10y = 20`?

Answer 1

`x=-5` and `y=-7`.

Explanation:

For this system of equations, I would adjust the first equation so that when you add the two equations together, the `y` is eliminated.

You can do so by multiplying everything by `2`:

`(-6x+5y=-5)" " times 2`

`-12x+10y=-10`

Now that this equation has a positive `10y` and the other equation has a `-10y`, adding the two problems would eliminate the `y` variable.

`{(-12x+10y=-10), (10x -10y= 20) :}`

Added together:

`-2x=10`

You can now solve for `x` by dividing both sides by `-2`.

`x=-5`

Now you can take any of the equations and enter in `-5` for `x` to solve for `y`.

`-6(-5)+5y=-5`

Multiply the `-6` and `-5`

`30+5y=-5`

Subtract `30` from both sides

`5y=-35`

Divide both sides by `5`

`y=-7`

There are many ways to solve systems of equations, but often it's easiest to find a way to adjust one of the equations so that when you add them together they eliminate one of the variables.