Determining Infinitely Many Solutions in a System of Linear Equations by Graphing

This video tutorial teaches how to determine if a system of two linear equations in two variables has infinitely many solutions by graphing. It reviews the slope-intercept form, explains how to graph equations, and discusses common mistakes. The tutorial provides examples of systems with infinitely many solutions, emphasizing the importance of converting equations to slope-intercept form and comparing slopes and y-intercepts.

What is the slope-intercept form of a linear equation?

• y = ax + b

• y = a/x + b

• y = ax^2 + bx + c

• y = mx + b

What does it mean if two linear equations have the same slope and y-intercept?

• They have no solutions.

• They have one solution.

• They have infinitely many solutions.

• They have two solutions.

How do you convert an equation to slope-intercept form?

• Divide both sides by y.

• Multiply both sides by x.

• Solve for y.

• Solve for x.

What is the slope of the equation y = 4x + 8?

• 0

• 4

• 8

• 2

If two equations are y = x + 1, what can be said about their graphs?

• They intersect at one point.

• They are parallel.

• They are the same line.

• They form a right angle.

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

• 0

• 1

• -1

• x

What property do two equations share if they have infinitely many solutions?

• Different slopes

• Different y-intercepts

• Same slope and y-intercept

• No common points