Question

What is the largest value of y in the solution set of the system of equations y = 2x^2 - x - 2 and y = x^2 + 3x - 5?

A) 3
B) 1
C) -1
D) 13

Answer 1

The largest value of y in the solution set of the given system of equations is 13.

Step-by-step explanation:

To find the largest value of y in the solution set of the system of equations:

y = 2x^2 - x - 2

y = x^2 + 3x - 5

We can solve these equations simultaneously by setting them equal to each other.

2x^2 - x - 2 = x^2 + 3x - 5

By rearranging and simplifying:

x^2 + 4x - 3 = 0

This quadratic equation can be factored as (x - 1)(x + 3)= 0.

The solutions are x = 1 and x = -3.

Substituting these values into either of the original equations, we can find the corresponding values of y. The largest value of y will be the higher value between the two solutions.

For x = 1: y = 2(1)^2 - 1 - 2 = -1

For x = -3: y = 2(-3)^2 - (-3) - 2 = 13

Therefore, the largest value of y in the solution set is 13 (option D).