Answer
The solution is $(-20, 360)$.
Work Step by Step
To solve this system of equations, we set the two equations equal to one another because they are both equal to the same number, $y$:
$x^2 + x - 20 = x^2 + 2x$
Subtract $x^2$ from both sides:
$x - 20 = 2x$
Add $20$ to both sides to move constants to the right side of the equation:
$x = 2x + 20$
Subtract $2x$ from both sides to move the variables to the left side of the equation:
$-x = 20$
Divide each side by $-1$ to solve for $x$:
$x = -20$
Now that we have the value for $x$, we can plug this value into either of the original equations to find the value for $y$. Let us use the second equation because we can deal with fewer terms:
$y = (-20)^2 + 2(-20)$
Let's simplify by multiplying out the terms:
$y = 400 - 40$
Subtract to solve for $y$:
$y = 360$
The solution is $(-20, 360)$.
