Predicting Solutions of Linear Equations by Inspection

This video tutorial teaches how to predict the number of solutions a system of linear equations has by inspection. It reviews the slope-intercept form of equations, explaining the concepts of slope and y-intercept. The tutorial discusses the three types of solutions for systems of linear equations: one solution, no solution, and infinitely many solutions. Through examples, it demonstrates how to identify these solutions by analyzing the slopes and y-intercepts of the equations. The video concludes with a summary of the key points covered.

What is the main goal of this lesson?

• To find the y-intercept of a line

• To graph linear equations

• To predict the number of solutions in a system of linear equations by inspection

• To solve linear equations

In the slope-intercept form of an equation, what does 'm' represent?

• The slope

• The x-intercept

• The constant term

• The y-intercept

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

• 1

• -1

• 0

• 2

How many types of solutions can a system of linear equations have?

• Four

• Three

• Two

• One

What does it mean if two lines in a system of linear equations are parallel?

• The system has two solutions

• The system has infinitely many solutions

• The system has no solution

• The system has one solution

If two equations in a system have the same slope and the same y-intercept, what can be concluded?

• The system has one solution

• The system has no solution

• The system has infinitely many solutions

• The system has two solutions

What is the slope of the equation y = -4(x + 4)?

• -4

• 4

• 0

• 1

For the equations y = x + 1 and y = 0.5x + 1, how many solutions does the system have?

• Infinitely many

• Two

• None

• One

What is the y-intercept of the equation y = -5x - 2?

• -2

• 2

• -5

• 5

If two lines have the same slope but different y-intercepts, what can be concluded about the system?

• The system has one solution

• The system has no solution

• The system has infinitely many solutions

• The system has two solutions