Linear Equations and Systems

The video tutorial covers solving systems of linear equations by graphing, using a bed and breakfast scenario to explain break-even analysis. It defines systems of linear equations, demonstrates graphing techniques to find solutions, and provides examples and practice problems to reinforce learning.

How much does your family charge per night to rent the bedroom in the bed and breakfast example?

• $500

• $100

• $60

• $10

What is the break-even point in the bed and breakfast example?

• 20 nights

• 15 nights

• 10 nights

• 5 nights

What is a system of linear equations?

• A polynomial equation

• A quadratic equation

• A set of two or more linear equations with the same variables

• A single linear equation

What is the solution to a system of linear equations?

• The x-intercept of the second equation

• The point where the graphs intersect

• The slope of the first equation

• The y-intercept of the first equation

In the example y = x - 1 and y = -x + 3, what is the solution?

• (2, 1)

• (0, 0)

• (3, 2)

• (1, 2)

For the equations y = -5x + 14 and y = x - 10, what is the point of intersection?

• (6, -4)

• (4, -6)

• (5, -5)

• (7, -3)

What is the y-intercept of the equation y = 2x + 1?

• 3

• 2

• 1

• 0

What is the solution to the system of equations y = x and y = 2x + 1?

• (0, 0)

• (2, 2)

• (-1, -1)

• (1, 1)

In the practice problems, what is the common denominator for the fractions 1/2, 1/3, 1/4, 1/5, and 1/6?

• 120

• 90

• 60

• 30

In the practice problems, what is the task for number 8?

• Solve a quadratic equation

• Create a system of equations with a given solution

• Graph a single linear equation

• Find the slope of a line