Exploring the Substitution Method for Systems of Equations

This video tutorial covers the substitution method for solving systems of equations. It begins with a brief review of the graphing method and then delves into the substitution method, explaining how to solve systems by substituting expressions. The tutorial includes several example problems to illustrate the process and concludes with a summary and contact information for further questions.

What are the three methods for solving systems of equations?

• Multiplication, division, subtraction

• Addition, subtraction, division

• Graphing, substitution, elimination

• Algebraic, geometric, trigonometric

What does a horizontal line represent in a graph of an equation?

• y = a constant value

• x = a constant value

• x = mx + b

• y = mx + b

What does it mean if two lines intersect on a graph?

• The system has one solution

• The lines are parallel

• The system has no solution

• The system has infinite solutions

How do you solve for x using the substitution method?

• By adding the two equations together

• By graphing the equations

• By eliminating one variable

• By substituting the value of y from one equation into the other

What is the solution to a system of equations represented by?

• An equation

• A graph

• A single number

• An ordered pair

What is the result of substituting y = 7x - 10 and y = -3?

• x = 1, y = -3

• x = -3, y = 1

• x = 0, y = 0

• No solution

In the substitution method, what do you do after equating the two expressions for y?

• Graph the equations

• Solve for x

• Multiply both sides by the coefficient of x

• Substitute x back into one of the equations

How do you check if an ordered pair is a solution to a system of equations?

• Add the equations together

• Multiply the equations

• Graph the equations and see if they intersect

• Substitute the values into both equations

What is the solution to the system where y = x - 8 and y = -4?

• x = 4, y = -4

• x = -4, y = 4

• x = 0, y = -8

• x = -8, y = 0

What does a solution of x = 7 and y = 42 indicate in a system of equations?

• The system has one unique solution

• The system has no solution

• The system has infinite solutions

• The equations are inconsistent