Solving Systems of Equations by Substitution

This video tutorial covers solving systems of equations using substitution. It begins with an introduction to the concept, followed by detailed examples demonstrating the substitution method. The tutorial also explores special cases such as infinitely many solutions and no solutions, providing a comprehensive understanding of the topic.

What is a system of equations?

• Two or more equations with the same variables

• A single equation with multiple variables

• A set of unrelated equations

• An equation with no variables

Which method can be used to check the solution of a system of equations?

• Only substitution

• Only graphing

• Only elimination

• Any of the methods: substitution, graphing, or elimination

In the substitution method, what should you do if you still have both x and y variables after substitution?

• Continue solving as usual

• Check for calculation errors

• Start over with a different method

• Ignore the extra variable

What is the solution to the system of equations where x = -4/3 and y = -1?

• (-1, -4/3)

• (4/3, 1)

• (-4/3, -1)

• (1, 4/3)

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

• Eliminate one variable

• Graph the equations

• Solve one equation for one variable

• Combine the equations

In the practice problem, what is the value of y when x = 2?

• 6

• 2

• 8

• 10

What is the total cost for a person taking both surfing lessons and parasailing at the vacation resort?

• $175

• $200

• $130

• $150

How many people went parasailing on Friday at the vacation resort?

• 25

• 20

• 16

• 30

What does it mean if the system of equations results in a true statement like -2 = -2?

• Incorrect solution

• No solution

• One solution

• Infinitely many solutions

What does it mean if the system of equations results in a false statement like 4 = -4?

• Incorrect solution

• Infinitely many solutions

• One solution

• No solution