Solving Systems of Equations by Substitution

The video tutorial explains systems of equations, which involve finding solutions that satisfy multiple equations. It covers three methods for solving these systems: graphing, substitution, and linear combinations, with a focus on the substitution method. The tutorial provides examples of systems with unique solutions, no solutions, and infinite solutions, emphasizing the importance of verifying solutions. It concludes with a summary of the substitution method's effectiveness when variables are isolated.

What is a system of equations?

• A single equation with one variable

• Two or more equations with two or more variables

• A set of equations that have no solutions

• An equation with no variables

Which method is NOT used to solve systems of equations?

• Factoring

• Graphing

• Substitution

• Linear Combinations

When is the substitution method particularly useful?

• When the equations are quadratic

• When graphing is not possible

• When one of the variables is isolated or easily isolated

• When the system has no solution

In the substitution method, what should you do after substituting one equation into another?

• Graph the equations

• Multiply the equations

• Solve for the remaining variable

• Add the equations together

What is the solution to the system if x = 2 and y = -1?

• (-1, 2)

• (2, -1)

• (2, 1)

• (1, -2)

What does it mean if simplifying a system of equations results in a false statement like 0 = 3?

• The system is inconsistent

• The system has exactly one solution

• The system has no solution

• The system has infinite solutions

What do parallel lines in the graph of a system of equations indicate?

• One solution

• No solution

• Infinite solutions

• Dependent equations

What does it mean if simplifying a system of equations results in a true statement like 4 = 4?

• The system is inconsistent

• The system has infinite solutions

• The system has exactly one solution

• The system has no solution

What is an identity in the context of systems of equations?

• A method of solving equations

• A unique solution

• A true statement that holds for all values of the variable

• A false statement

Which method is best when one variable is isolated or nearly isolated?

• Graphing

• Linear Combinations

• Factoring

• Substitution