Solving Systems of Equations Using the Substitution Method

The video tutorial explains how to solve a system of equations using the substitution method. It begins with an introduction to the concept of solving systems, highlighting the possibility of unique, no, or infinite solutions. The tutorial then outlines the steps for the substitution method: solving for a variable, substituting into the other equation, solving the resulting equation, and performing back substitution. An example problem is solved step-by-step, and the solution is verified. The video concludes by connecting the solution to a graphical representation, showing the point of intersection of the equations.

What does it mean to solve a system of equations?

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

• To graph the equations on a coordinate plane.

• To determine the slope of the equations.

• To find the y-intercept of the equations.

Which of the following is NOT a possible outcome when solving systems of equations graphically?

• Two unique solutions

• No solutions

• One unique solution

• An infinite number of solutions

What is the first step in the substitution method?

• Check the solution.

• Solve for a variable in one of the equations.

• Substitute the isolated variable into the other equation.

• Solve the equation with one variable.

What do you do after solving for a variable in one of the equations in the substitution method?

• Check the solution.

• Graph the equations.

• Perform back substitution.

• Substitute the isolated variable into the other equation.

In the given example, what is the value of x after solving the equation?

• -4

• 4

• -8

• 8

What is the next step after finding the value of x in the substitution method?

• Graph the equations.

• Check the solution.

• Solve for another variable.

• Perform back substitution to find the value of y.

What is the value of y in the given example after performing back substitution?

• -4

• 8

• 4

• -8

How can the solution of a system of equations be verified?

• By determining the y-intercept of the equations.

• By finding the slope of the equations.

• By solving another system of equations.

• By checking if the values satisfy both equations.

What should be the point of intersection when graphing the two lines in the given example?

• (4, 4)

• (-4, 4)

• (4, -8)

• (-4, -8)

What does the point of intersection represent in the context of solving systems of equations graphically?

• The midpoint of the lines.

• The slope of the lines.

• The y-intercept of the lines.

• The solution to the system of equations.