Exploring Systems of Linear Equations

The video tutorial introduces systems of equations, explaining that they consist of two or more equations working together. It demonstrates how to find solutions using graphing, where the intersection point of the lines represents the solution. The tutorial also covers verifying solutions through substitution, ensuring the ordered pair satisfies both equations.

What is a system of equations?

• A single equation with one variable

• A set of inequalities

• Two or more equations that work together

• An equation with no solution

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

• x + y = 5

• 2x - 3y = 7

• x + 2y = 11 and 3x - y = 4

• x^2 + y^2 = 25

What is the solution to a system of equations?

• A single number

• An ordered pair that satisfies both equations

• A set of inequalities

• A polynomial

How can you solve a system of equations using a graph?

• By substituting values

• By finding the intersection point of the lines

• By solving each equation separately

• By using a calculator

In the given graph, what do the blue and red lines represent?

• Two different equations in the system

• Two different systems

• Two different inequalities

• Two different functions

What is the solution to the system where the blue line is 3x + 2y = 4 and the red line is -x + 3y = -5?

• (2, -1)

• (1, 2)

• (-2, 1)

• (0, 0)

How can you verify the solution to a system of equations?

• By using a different method

• By solving the equations separately

• By substituting the solution into both equations

• By graphing the equations again

What is the result when you substitute (2, -1) into the first equation 3x + 2y = 4?

• 6 - 2 = 4

• 6 + 2 = 8

• 3 - 2 = 1

• 3 + 2 = 5

What is the result when you substitute (2, -1) into the second equation -x + 3y = -5?

• 2 + 3 = 5

• 2 - 3 = -1

• -2 - 3 = -5

• -2 + 3 = 1