Algebra-1

To find the solution to the system of equations:

1) y = x² - x - 90
2) y = x + 30

We can set the expressions for y equal to each other since they both represent y:

x² - x - 90 = x + 30

Now, let's rearrange the equation to the standard form:

x² - x - x - 90 - 30 = 0

x² - 2x - 120 = 0

To solve this quadratic equation, we can factorize it:

(x - 12)(x + 10) = 0

Now, we can apply the zero product property and set each factor equal to zero:

x - 12 = 0   or   x + 10 = 0

Solving the first equation, we find:

x - 12 = ...