Simplify the System

Question

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

Answer 1

Natalie,

 

You have 2 equations in 2 unknowns.  Set the y's equal for a solution, simplify, and get the following quadratic in x:

 

x2 - 5x - 19 = 0

 

Solve this using the quadratic formula:  x = {[+5 ± √101]/2} = 7.52494 & -2.52494.

 

Then use the simpler linear equation (y = 3x + 27) to compute the corresponding y's.  You'll get the same y's using the other equation for y but it will require a bit more work,

 

For x₁ = + 7.52494 ,   y = 49.5748

For x₂ = -  2.52494 ,   y = 19.4252

 

So your answer is that x₂ gives you the smallest y.