Solving Systems of Equations

The video tutorial explains how to solve a system of two linear equations using the substitution method. It begins with solving one equation for a variable, substituting it into the second equation, and solving for the other variable. The solution is verified both algebraically and graphically, demonstrating that the ordered pair satisfies both equations and represents the point of intersection on a graph.

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

• Substitution and Graphing

• Substitution and Elimination

• Elimination and Factoring

• Graphing and Factoring

What is the first step in solving the system using substitution?

• Eliminate one variable

• Graph the equations

• Solve the first equation for y

• Solve the second equation for x

After substituting y in the second equation, what type of equation do we solve?

• An equation with two variables

• A cubic equation

• A quadratic equation

• An equation with one variable

What is the value of x after solving the equation?

• x = -4

• x = 4

• x = -3

• x = 3

What is the value of y after performing back substitution?

• y = -4

• y = 4

• y = -3

• y = 3

How do we verify the solution algebraically?

• By graphing the solution

• By solving another system

• By checking if the solution satisfies both equations

• By factoring the equations

What is the result when substituting x = -3 and y = 4 into the first equation?

• The equation is not satisfied

• The equation is satisfied

• The result is zero

• The result is negative

What is the result when substituting x = -3 and y = 4 into the second equation?

• The result is negative

• The result is zero

• The equation is satisfied

• The equation is not satisfied

What does the point of intersection represent in the graphical method?

• A random point on the graph

• The midpoint of the lines

• The origin

• The solution to the system

What are the coordinates of the point of intersection?

• (3, -4)

• (-3, 4)

• (3, 4)

• (-3, -4)