SOLUTION: Use substitution with the two equations and determine the points of intersection. Show all work. y=x^2-1 y=x

Question 228283: Use substitution with the two equations and determine the points of intersection. Show all work.
y=x^2-1
y=x
Answer by drj(1380) (Show Source): You can put this solution on YOUR website!
Use substitution with the two equations and determine the points of intersection. Show all work.

Equation A
Equation B

Step 1. Substitute Equation B into Equation A

Subtract x from both sides of the equation

Step 2. To solve, use quadratic formula given as

where a=1, b=-1 and c=-1.

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=5 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 1.61803398874989, -0.618033988749895. Here's your graph:

Step 3. ANSWER: One solution is x=1.618 and y=1.618 or (1.618, 1.618) and the other solution is x=-0.618 and y=-0.618 or (-0.618,-0.618)

Here's a graph between the the line and parabola :

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J
http://www.FreedomUniversity.TV

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