solve the system of equations y=2x y=x^2-15

Answer 1

Since both equations are already set equal to y, we can solve the system by setting the right hand sides equal to each other:

2x=x^2-15

Since there's a quadratic term, it's easiest to move everything to one side:

0 = x^2-2x-15

From here, we can factor the right hand side as (x-5)(x+3) to see the solutions are x = 5 and x = -3 [You could also use the quadratic formula to arrive at the same values.

Once we have the x's, just plug them back into either equation to find the corresponding y's. This gives us:

when x = 5, y = 10

when x = -3, y = -6