Solving Systems of Equations

The video tutorial explains how to solve a system of equations using the substitution method. It begins by substituting one equation into another to form a quadratic equation, which is then factored to find the x-values. The corresponding y-values are determined to form ordered pairs, which are verified graphically as points of intersection on a coordinate plane. The tutorial concludes by confirming the solutions are correct.

What is the purpose of solving a system of equations?

• To find the values of x and y that satisfy both equations.

• To determine the slope of the line.

• To calculate the area under the curve.

• To find the maximum value of y.

Which method is used to solve the given system of equations?

• Graphing

• Substitution

• Matrix method

• Elimination

What type of equation is formed after substitution?

• Linear equation

• Exponential equation

• Quadratic equation

• Cubic equation

What is the first step in factoring the quadratic equation?

• Add a constant to both sides

• Multiply both sides by x

• Factor out the greatest common factor

• Divide by the coefficient of x

What are the possible x values found after factoring?

• x = 1 and x = -1

• x = 0 and x = -3

• x = 2 and x = -2

• x = 3 and x = -3

How do you find the corresponding y values for the x values?

• By substituting x values into one of the original equations

• By using the quadratic formula

• By solving a new system of equations

• By graphing the equations

What is one of the ordered pair solutions to the system?

• (0, -2)

• (0, 3)

• (-3, 7)

• (-3, -7)

What is the other ordered pair solution to the system?

• (2, 0)

• (3, 0)

• (-2, 0)

• (0, 2)

How can the solutions be verified graphically?

• By checking the slope of the lines

• By finding the points of intersection on the graph

• By drawing a tangent line

• By calculating the area between the curves

What do the points of intersection represent in the graph?

• The maximum values of the functions

• The solutions to the system of equations

• The average rate of change

• The x-intercepts of the functions