Understanding the Substitution Method in Solving Systems of Equations

The video tutorial explains how to solve a system of equations using the substitution method. It begins by introducing the concept of finding an ordered pair that satisfies both equations. The tutorial then outlines the steps of the substitution method, including solving one equation for a variable and substituting it into the other equation. The process is demonstrated with an example, leading to a scenario where the variables simplify out, resulting in a true statement, indicating infinite solutions. The video concludes by verifying the result graphically, showing that the equations produce the same line.

What is the main goal when solving a system of equations using the substitution method?

• To find a single solution for x

• To graph the equations

• To find an ordered pair that satisfies both equations

• To eliminate one of the equations

What is the first step in the substitution method?

• Checking for infinite solutions

• Graphing the equations

• Solving one equation for one variable

• Eliminating one variable

In the given system, which equation is already solved for y?

• Neither equation

• Both equations

• Equation two

• Equation one

What do you achieve by substituting the expression for y into equation one?

• An equation with two variables

• An equation with one variable

• A solution for y

• A graph of the equations

After substitution, what is the next step in solving the equation?

• Graph the equation

• Solve for y

• Solve for x

• Check for no solutions

What does it mean if the variables simplify out and you are left with a true statement?

• There are infinite solutions

• The equations are inconsistent

• There is one solution

• There is no solution

What does the equation 10 = 10 indicate about the system of equations?

• The system has no solution

• The system is inconsistent

• The system has a unique solution

• The system has infinite solutions

What happens graphically when a system of equations has infinite solutions?

• The lines are parallel

• The lines are perpendicular

• The lines intersect at one point

• The lines coincide

What does it mean if the two equations produce the same line?

• The system has infinite solutions

• The system is inconsistent

• The system has a unique solution

• The system has no solution

How can you verify that a system of equations has infinite solutions?

• By checking for parallel lines

• By finding a single solution

• By solving for y

• By graphing and seeing the lines coincide