Algebra Know-It-ALL

524 Review Questions and Answers

• Plug the root(s) into one of the morphed original equations, and calculate the corre-
  sponding value(s) of the dependent variable.


• Express the solution(s) as one or more ordered pairs.

Question 27-2

Consider the following pair of quadratic equations as a two-by-two system:

y=x^2

and

y=−x^2

How can we find the real solutions of this system?

Answer 27-2

Let’s call x the independent variable. Then we can mix the right sides of the equations to get

x^2 =−x^2

Adding x^2 to each side, we get

2 x^2 = 0

Dividing through by 2 gives us

x^2 = 0

This equation has one real root, x= 0. When we plug this into either of the original equations,

we get y= 0. Therefore, the single real solution to this system is (0,0).

Question 27-3

Consider the following pair of quadratic equations as a two-by-two system:

y=x^2 − 1

and

y=−x^2 + 1

How can we find the real solutions of this system?

Answer 27-3

Again, let x be the independent variable. When we mix the right sides, we get

x^2 − 1 =−x^2 + 1