Systems of Linear Equations

This video tutorial covers systems of linear equations, including checking solutions, solving by graphing, and applying these concepts to real-life problems. It provides examples to illustrate how to determine if an ordered pair is a solution, how to graph equations to find intersections, and how to use equations to solve practical problems like pricing.

What is a system of linear equations?

• A single linear equation with multiple solutions

• A set of equations with different variables

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

• A quadratic equation with two variables

Which of the following is an example of a system of linear equations?

• x^2 - y = 5

• x^2 + y^2 = 1

• x + y = 7 and 2x - 3y = -11

• x - y = 0

How can you determine if an ordered pair is a solution to a system of equations?

• By solving the equations algebraically

• By graphing the equations

• By substituting the pair into both equations and checking if both are true

• By checking if it satisfies at least one equation

In Example 1, what is the result of substituting the ordered pair (2, 5) into the first equation x + y = 7?

• 2 + 5 = 10

• 2 + 5 = 7

• 2 + 5 = 6

• 2 + 5 = 8

What is the solution to the system of equations in Example 2 when solved by graphing?

• (2, 5)

• (0, 0)

• (3, 1)

• (1, 3)

In Example 3, what is the price per bundle of shingles?

• $50

• $32

• $20

• $40

In Example 3, what is the price per roll of roofing paper?

• $15

• $20

• $25

• $10