Question

What are the solutions of the system?
y=x+5
y=x^2-x+2

Answer 1

Combine the equations to get: \[x^{2} -2x -3 = y. \]

Answer 2

Oops, I meant set them equal to each other.

Answer 3

Since you have y equal to two different expressions in x, set the two expressions equal to each other.

\(x + 5 = x^2 - x + 2\)

Now bring all terms to the left side, and solve the quadratic equation in x.

Then substitute each solution in the first original equiation to get a y value.

You should end up with two ordered pairs.