Understanding Coordinate Systems and Solutions

This video tutorial explains how to solve a system of nonlinear equations using the substitution method. The instructor demonstrates solving the equations algebraically and verifies the solutions graphically. The process involves substituting one equation into another, solving for Y, and then using back substitution to find the corresponding X values. The tutorial concludes with a graphical check to confirm the solutions by identifying intersection points on a coordinate plane.

What are the two methods mentioned for solving a system of nonlinear equations?

• Matrix Method and Graphing

• Substitution and Elimination

• Graphing and Factoring

• Completing the Square and Quadratic Formula

In the substitution method, what is the first step to solve the given system of equations?

• Solve for Y squared in the second equation

• Solve for X squared in the first equation

• Solve for X in the second equation

• Solve for Y in the first equation

After substituting X squared in the second equation, what is the next step?

• Solve for Y

• Check the solution

• Solve for X

• Graph the equation

What value of Y is obtained after solving the equation 6 + 6Y = 18?

• Y = 1

• Y = 3

• Y = 2

• Y = 4

What are the possible values of X when Y equals 2?

• X = 4 or -4

• X = 0

• X = 6 or -6

• X = 2 or -2

How are solutions represented when given as ordered pairs?

• Both coordinates are the same

• Only X coordinate is given

• X coordinate first, then Y coordinate

• Y coordinate first, then X coordinate

What is the significance of the first coordinate in an ordered pair?

• It represents the difference between X and Y

• It represents the Y value

• It represents the X value

• It represents the sum of X and Y

What is the purpose of graphing the original equations on a coordinate plane?

• To calculate the area under the curve

• To determine the y-intercept

• To verify the solutions by finding points of intersection

• To find the slope of the lines

Where do the graphs of the equations intersect on the coordinate plane?

• At the origin

• At two points

• At one point

• They do not intersect

What are the coordinates of the intersection points in the first and second quadrants?

• (+2, +4) and (-2, +4)

• (+4, +2) and (-4, +2)

• (+2, -4) and (-2, -4)

• (+4, -2) and (-4, -2)