Solving Non-Linear Equations in Algebra

This video tutorial by Mrs. Out covers Chapter 9, Lesson 6 on solving systems of nonlinear equations. It explains three methods: graphing, substitution, and elimination. The tutorial includes examples with quadratic and linear equations, demonstrating how to find solutions or determine if no solutions exist. The video also provides practice problems and encourages students to solve them independently.

What are the three methods to solve systems of nonlinear equations?

• Addition, subtraction, division

• Graphing, substitution, elimination

• Integration, differentiation, factoring

• Multiplication, division, subtraction

What is the vertex of the quadratic equation discussed in the first example?

• (1, 1)

• (-2.5, -0.25)

• (2, 3)

• (0, 0)

In the second graphing example, what is the axis of symmetry found using the formula -B/2A?

• 2

• -0.5

• 1

• 0

What does the substitution method involve?

• Eliminating variables by adding equations

• Replacing one variable with another

• Drawing graphs to find intersections

• Using derivatives to solve equations

What is the result when using the substitution method for the equation 6 - 2 = x^2?

• x = ±5

• x = ±2

• x = ±3

• x = ±4

What is the outcome when graphing two equations that result in a negative discriminant in the quadratic formula?

• One intersection point

• Two intersection points

• No intersection points

• Infinite intersection points

In the elimination method, what do you aim to eliminate?

• The quadratic term

• The linear term

• One of the variables

• The constant term

What is the result of the elimination method for the equation set where the discriminant is negative?

• Infinite solutions

• One solution

• Two solutions

• No solutions

What are the solutions for the system where x squared equals 4 after using elimination?

• x = ±1

• x = ±2

• x = ±3

• x = ±4

What is the y-value when x = 2 in the final elimination example?

• y = 8

• y = 7

• y = 6

• y = 5