Determining the Number of Solutions in Equations

This video tutorial covers lesson 62 on systems of equations, focusing on determining the number of solutions by comparing slopes and y-intercepts. It explains how to identify whether a system has no solution, one solution, or infinite solutions. The tutorial includes examples and practice problems to reinforce the concepts.

What are the three types of solutions that can be found when graphing systems of equations?

• One solution, no solution, infinite solutions

• One solution, no solution, two solutions

• No solution, two solutions, infinite solutions

• One solution, two solutions, infinite solutions

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

• They intersect at one point

• They have no solution

• They have one solution

• They have infinite solutions

What does it mean if two lines have different slopes and different y-intercepts?

• They have infinite solutions

• They have no solution

• They are parallel

• They have one solution

When two lines have the same slope and the same y-intercept, what is the number of solutions?

• No solution

• Two solutions

• One solution

• Infinite solutions

What is the slope of the line represented by the equation y = -x + 5?

• -1

• 1

• 5

• 0

If a line has a slope of 3/4 and a y-intercept of 0, what is its equation in slope-intercept form?

• y = 3/4x - 0

• y = 3/4x + 0

• y = 3/4x

• y = 3/4

How do you convert the equation 2y = 4x + 16 to slope-intercept form?

• Divide both sides by 2

• Multiply both sides by 2

• Add 16 to both sides

• Subtract 4x from both sides

What is the y-intercept of the line passing through the points (0, 4) and (3, 2)?

• 2

• 3

• 5

• 4

If two lines have the same slope but different y-intercepts, what is their relationship?

• They are perpendicular

• They are parallel

• They intersect at one point

• They have infinite solutions

What is the slope of the line passing through the points (3, -3) and (9, -7)?

• 4/6

• 2/3

• -2/3

• -4/6