Solve the system of equations by the substitution method.

Question

y=x²-4x-2

y=x²+18

Answer 1

I always encourage checking the answers you get.

I'd go that "extra mile" on the solution above, and make sure (-5, 43) works in both equations.

1) y=x²-4x-2

43 = (-5)² - 4(-5) - 2

43 = 25 + 20 - 2

43 = 43

2) y=x²+18

43 = (-5)² + 18

43 = 25 + 18

43 = 43

Both check out!

Answer 2

You have two expressions involving x that are both equal to y. So replace y in one of the equations with its equivalent expression in terms of x. This gives:

x² - 4x - 2 = x² + 18

Subtracting x² from both sides leaves:

-4x - 2 = 18

-4x = 20

x = -5

That means the two parabolas intersect at a point with an x-coordinate (abscissa) equal to -5.

To find the corresponding y-coordinate substitute - 5 for x in one of the given equations:

y = (-5)² + 18 = 43

So the one point where these parabolas intersect is (-5, 43).

Take a look here to see the result:

desmos.com/calculator/w9fmwuvxu2