Word Problem

Question

What is the smallest value of y in the solution of the system 
y= x²-2x+8 and y=3x+2

I need the steps and the answer to this problem pleasee

Answer 1

3x + 2 = x² -2x +8 (set both halves equal)

x²-5x+6 = 0 (put everything on the same side)

(x-2)(x-3) = 0 (factor)

x=2 OR x=3

 

Plug both of those into either equation to find the smallest value of y.  I'll use the linear one, as the math is easier.

 

y(2) = 3(2)+2 = 8

y(3) = 3(3)+2 = 11

 

So the answer is 8, because it is the smaller of the two y values.