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