Solving Nonlinear Equations and Parabolas

This video tutorial explains how to solve a system of nonlinear equations using substitution. It demonstrates the algebraic process of solving the equations and finding solutions, including the use of absolute values to understand why there are two solutions. The tutorial also covers back substitution to find corresponding y-values and verifies the solutions graphically by showing the intersection points of the parabolas on a coordinate plane.

What method is used to solve the system of nonlinear equations in the video?

• Elimination method

• Graphical method

• Matrix method

• Substitution method

What is the result of substituting x squared - 9 for y in the second equation?

• x squared + 9 = 9 - x squared

• x squared + 9 = 9 + x squared

• x squared - 9 = 9 + x squared

• x squared - 9 = 9 - x squared

After simplifying the equation, what is the value of x squared?

• 0

• 9

• 18

• 3

Why do we consider both positive and negative solutions for x?

• Because x can only be positive

• Because x squared can be negative

• Because x can only be negative

• Because the square root of x squared is the absolute value of x

What is the y value when x is 3?

• -9

• 9

• 0

• 3

What is the y value when x is -3?

• -9

• 0

• 3

• 9

How many solutions does the system of nonlinear equations have?

• One solution

• No solution

• Two solutions

• Three solutions

What shape do the graphs of the equations form?

• Lines

• Circles

• Parabolas

• Ellipses

Where do the parabolas intersect on the graph?

• At (3,3) and (-3,-3)

• At (3,0) and (-3,0)

• At (0,0) and (0,3)

• At (0,3) and (0,-3)

What is the significance of the intersection points of the parabolas?

• They represent the minimum points of the parabolas

• They represent the maximum points of the parabolas

• They represent the axis of symmetry

• They represent the solutions to the system of equations