Exploring Substitution in Systems

The video tutorial covers solving systems of equations using the substitution method. It begins with a warm-up exercise, followed by a review of solving systems graphically. The main focus is on solving systems algebraically using substitution, with detailed steps and examples provided. The tutorial concludes with additional practice problems to reinforce the concepts.

What method is introduced for solving systems of equations?

• Elimination

• Matrix

• Substitution

• Graphing

What is the first step in solving systems of equations using substitution?

• Solve for one variable

• Graph the equations

• Combine like terms

• Substitute one equation into the other

What does the solution to a system of equations represent graphically?

• The slope

• The x-intercept

• The point where two lines intersect

• The y-intercept

After substituting and solving for one variable, what is the next step?

• Solve for the second variable

• Graph the solution

• Check the solution

• Rewrite the original equations

In the first example, what is the value of x found?

• -1/4

• -11

• 1

• 3

What is the ordered pair that represents the solution in the first example?

• (1, -3)

• (-1, 5)

• (-1/4, 2)

• (3, -11)

How do you confirm the solution to a system of equations?

• By substituting back into one equation

• By solving another system

• Graphically, where the lines intersect

• By checking the slope

In the additional examples, what is the primary method used to solve the systems?

• Elimination

• Graphing

• Substitution

• Matrix

What is the value of y in the final example?

• 5

• 1

• -3

• 2

What is the significance of the ordered pair in the context of systems of equations?

• It is the solution where the two equations intersect

• It shows the maximum value of the equations

• It represents the slope of the lines

• It indicates the y-intercept of the graph