Solving Systems of Equations by Substitution

This video tutorial covers solving systems of equations using the substitution method. It begins with an introduction to the method, compares it to graphing, and provides a detailed example problem. Students are given a practice problem to solve, and special cases like infinitely many solutions and no solutions are discussed. The tutorial also explores real-world applications through word problems, concluding with a recap of key points.

What is the main focus of Algebra Lesson 4.2?

• Solving single-variable equations

• Solving quadratic equations

• Solving systems of equations by substitution

• Solving systems of equations by graphing

When is the substitution method particularly useful?

• When you have a variable with a coefficient of 10

• When you have a variable with a coefficient of 5

• When you have a variable with a coefficient of 1

• When you have a variable with a coefficient of 0

In the example problem, what is the value of x after solving 3x - 8(6x + 7) = 4?

• 14

• 1/3

• Negative 2

• Negative 1 and 1/3

What is the y-coordinate in the solution to the example problem?

• Negative 2

• Negative 1

• 2

• 1

What is the ordered pair solution for the practice problem with equations y = 2x - 1 and 2x + 3y = -7?

• (-1/2, -2)

• (1/2, 2)

• (-1, -1/2)

• (1, -2)

What does it mean if you end up with a true statement like -2 = -2 after solving a system of equations?

• No solution

• Infinitely many solutions

• One solution

• Two solutions

What does it mean if you end up with a false statement like 4 = -4 after solving a system of equations?

• No solution

• Infinitely many solutions

• One solution

• Two solutions

In the word problem about Nate's lawn mowing business, what are his expenses?

• $400 for the lawnmower and $4 per lawn

• $300 for the lawnmower and $3 per lawn

• $100 for the lawnmower and $1 per lawn

• $200 for the lawnmower and $2 per lawn

At approximately how many lawns will Nate's revenue exceed his expenses?

• 7 lawns

• 10 lawns

• 8 lawns

• 9 lawns

For the amusement park problem, at how many rides will the cost be the same at both parks?

• 20 rides

• 26 rides

• 24 rides

• 22 rides