Question

A system of equations is shown below.

y = 2x2 - x - 2

y = x2 + 3x - 5

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

How do I solve these equations?

Answer 1

the first equation the y intercept is -2

Answer 2

Answer is 13.

Explanation:

EQ 1: y = 2x^2-x-2

EQ2: y = x^2+3x -5

Set the two equation equal to each other:

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

Simplify:

x^2 -4x +3 = 0

(x - 3 ) (x - 1) = 0

Solutions:

x = 3 and x= 1

Plug these values into each of the original equations and see which on gives you the highest value.

Solution set:

y={13, -1, 13, -1}

Answer is 13