Solving Systems of Linear Equations by Graphing

The video tutorial covers algebra section 5.1, focusing on solving systems of equations by graphing. It begins with an introduction to systems of linear equations and their solutions. The tutorial then explains how to determine if an ordered pair is a solution to a system. The main method discussed is solving systems by graphing, with detailed steps and examples provided. The video concludes with a real-world application problem, demonstrating how to set up and solve a system of equations to find the number of exercises in math and science.

What is a system of linear equations?

• A single linear equation

• A quadratic equation

• A set of two or more linear equations in the same variable

• A polynomial equation

What does it mean for an ordered pair to be a solution to a system of linear equations?

• It satisfies all the equations in the system

• It satisfies at least one equation

• It satisfies none of the equations

• It satisfies only one of the equations

What is the first step in solving a system of equations by graphing?

• Find the y-intercept

• Check the solution

• Graph both equations on the same coordinate plane

• Solve for x

When graphing the equation y = -2x + 5, what is the y-intercept?

• 0

• 1

• -2

• 5

In the equation y = 4x - 1, what is the slope?

• 0

• 1

• -1

• 4

What is the point of intersection for the equations y = -2x + 5 and y = 4x - 1?

• (3, 1)

• (2, -1)

• (0, 5)

• (1, 3)

What is the slope of the equation y = x - 2?

• -1

• 0

• -2

• 1

How do you convert the equation 2x + y = 5 to slope-intercept form?

• Subtract y from both sides

• Add 2x to both sides

• Subtract 2x from both sides

• Divide by 2

In the application problem, what is the total number of math and science exercises?

• 24

• 18

• 6

• 12

In the application problem, if there are 6 more math exercises than science exercises, which equation represents this relationship?

• x = y - 6

• y = x + 6

• x = y + 6

• y = x - 6