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 and potential outcomes of solving systems of equations. The tutorial then demonstrates solving for X by substituting the expression for Y from the second equation into the first. After finding X, the value is substituted back to find Y, resulting in an ordered pair solution. The solution is verified both algebraically and graphically, confirming its accuracy. The video concludes with a graphical representation of the solution, showing the intersection point of the two equations.

What is the substitution method primarily used for?

• Solving a system of equations

• Solving quadratic equations

• Finding the derivative of a function

• Calculating the area of a triangle

What is the first step in the substitution method?

• Multiplying the equations

• Adding the equations together

• Solving one equation for one variable

• Graphing the equations

In the given system, what is the expression for Y?

• Y = 3X + 4

• Y = -X + 4

• Y = X + 4

• Y = -3X + 4

What operation is performed after substituting Y in the first equation?

• Clearing the parentheses by distributing

• Subtracting the equations

• Adding the equations

• Graphing the equations

What is the value of X after solving the equation?

• X = 7

• X = -3

• X = -7

• X = 3

How do you find the value of Y once X is known?

• By subtracting X from the first equation

• By adding X to the second equation

• By substituting X into the second equation

• By substituting X into the first equation

What is the ordered pair solution for the system of equations?

• (-3, 7)

• (-3, -7)

• (3, -7)

• (3, 7)

What does it mean if a system of equations has one unique solution?

• The system is inconsistent

• The system is consistent and independent

• The system is dependent

• The system has infinite solutions

What is verified by graphically checking the solution?

• The point of intersection matches the solution

• The equations are identical

• The solution is incorrect

• The equations are parallel

What is the significance of the point of intersection in the graph?

• It shows where the lines are parallel

• It indicates the solution to the system

• It shows the midpoint of the lines

• It indicates the lines are perpendicular