Question

How do you find the solution of the system of equations `y= x^2 + 5` and `y = 2x + 4`?

Answer 1

Since you have already been given two expressions for `y`, why not combine them to eliminate `y` and solve for `x`?

`x^2 + 5 = 2x + 4`

Subtract `2x + 4` from both sides to give the quadratic:
`x^2 - 2x + 1 = 0`

You don't need to use the general quadratic solution to simply notice that `0 = x^2 - 2x + 1 = (x - 1)(x - 1)`.

So there's just one (repeated) solution with `x = 1`.

Substitute `x = 1` into either of the original equations to get `y = 6`.