Question

How do you solve the system of equations `y= 3x - 2` and `y = 2x - 8`?

Answer 1

`x = -6` and `y = -20`

Explanation:

To solve this system of equations, you can use a method called substitution, where you put `y` in terms of `x`, and replace `y` in the other equation for `y` in terms of `x`. You can also do this with `x` in terms of `y`.

Fortunately, both are already in terms of `y`.

`y=3x-2` and `y=2x-8`, so because `y=y`: `3x-2=2x-8`.

Then by subtracting `2x` off each side:

`3x-2-2x=2x-8-2x => x-2=-8`

And adding `2` to each side:

`x-2+2=-8+2 => x=-6`

So we have the value of `x`, which we can put back into the equation for `y` in terms of `x`:

`y = 3x-2=3xx-6-2 = -20`, hence our value for `y`.

You can then check this by putting the values into the two original equations and making sure they add up.