Question

A system of equations is shown below.

y = 3x + 9

y = x^2 - 1

What is the largest value of y in the solution set of the system?

A. -2

B. 24

C. 3

D. 5

Answer 1

To find the largest value of y in the solution set of the system of equations, we need to determine the maximum value of y. The largest value of y is 24.

Step-by-step explanation:

To find the largest value of y in the solution set of the system of equations, we need to determine the maximum value of y.

We can start by equating the two equations:

3x + 9 = x^2 - 1

Rearranging the equation, we get:

x^2 - 3x -10 = 0

Factoring the quadratic equation, we have:

(x - 5)(x + 2) = 0

So, the possible values of x are 5 and -2.

Plugging these values of x back into the original equation, we get the corresponding values of y:

When x = 5, y = 3(5) + 9 = 24

When x = -2, y = 3(-2) + 9 = 3

The largest value of y in the solution set of the system is 24.