y = x^2 + 6x - 8, y = 4x + 7 What is the sum of the y value(s) of the solution set?

Answer 1

Finding the "solution" to a system of functions means finding the x and y values that work with all the functions in the system. In other words, you are looking for the intersection point(s) of the functions, the places where the y's equal each other and the x's equal each other. So, since the y's must equal each other, we can just set the right hand portions of the functions together.

x² + 6x - 8 = 4x + 7 [to solve a quadratic equation, set it equal to zero

x² + 2x - 15 = 0 [try factoring, in this case that works

(x + 5)(x - 3) = 0 [set each piece equal to zero

x = -5 and x = 3 to find the y values, plug these x values in to one of the equations

y = 4(-5) + 7 = -13 so this solution point is (-5, -13)

y = 4(3) + 7 = 19 so this solution point is (3, 19)

The sum of the y values is -13 + 19 = 6

Answer 2

Find (x,y) points that satisfy both equations

x^2 + 6x - 8 = 4x + 7 [set equal to find solution (point(s) that satisfy both)

x^2 + 2x -15 = 0 [collect terms on left side]

(x-3)(x+5) = 0 [factor]

Either x=3 or x=5 or both [ Multiplicative Property of Zero]

At x = 3, y = 19 point (3,19)

At x = -5, y= -13 point (-5,-13)

Sum of y values of solution set is 19 - 13 = 6