Algebra-1

To find the solution to the system of equations:

1) y = x² - 9x + 18
2) y = x - 3

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

x² - 9x + 18 = x - 3

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

x² - 9x - x + 18 + 3 = 0

x² - 10x + 21 = 0

To solve this quadratic equation, we can factorize it:

(x - 3)(x - 7) = 0

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

x - 3 = 0   or   x - 7 = 0

Solving the first equation, we find: