Question

How do you find the solution of the system of equations `y= x^2-4` and `y= x-2`?

Answer 1

You can isolate one variable in one equation and substitute its value in the other one. Let's do it.

Let's get the value of `y` in the first equation and substitute it in the second one and, then, find `x`:

`x^2-4=x-2`
`x^2-x-2=0`

Using Bhaskara:

`(1+-sqrt(1^2-4(1)(-2)))/2*1`
`(1+-3)/2`
`x_1=2` and `x_2=-1`

Now we have these values for `x`, let's find the values of `y` - using the first equation:

`y_1=(2)^2-4=0`
`y_2=(-1)^2-4=-3`

So, your answers are:

`y=0` when `x=2`
`y=-3` when `x=-1`