Graphing Systems of Equations Mastery

In this video, Mr. Pasus introduces graphing systems of equations, demonstrating how to graph and interpret solutions. He covers three scenarios: intersecting lines with a single solution, parallel lines with no solution, and overlapping lines with infinite solutions. The video emphasizes understanding the graphical representation of systems and identifying solutions based on line interactions.

What is the first step in graphing systems of equations?

• Determine the y-intercept

• Calculate the slope

• Graph both equations on the same graph

• Find the x-intercept

What is the y-intercept of the first line in the first example?

• 9

• 7

• 6

• 8

How do you determine the solution to a system of equations by graphing?

• Find the point where the lines intersect

• Determine the x-intercepts of the lines

• Calculate the slopes of the lines

• Find the y-intercepts of the lines

What does it mean if two lines on a graph are parallel?

• They intersect at multiple points

• They intersect at one point

• They have no solution

• They have infinitely many solutions

In the second example, what is the slope of the lines?

• 3

• 2

• 4

• 1

What is the y-intercept of the second line in the second example?

• 6

• 2

• 8

• 4

What does it mean if two lines on a graph overlap completely?

• They intersect at multiple points

• They have infinitely many solutions

• They have no solution

• They intersect at one point

In the third example, what is the slope of the lines?

• 3

• 2

• 1

• 4

What is the y-intercept of the first line in the third example?

• -7

• -6

• -5

• -4

What are the three possible outcomes when graphing systems of equations?

• No solution, two solutions, infinitely many solutions

• One solution, two solutions, three solutions

• One solution, two solutions, no solution

• One solution, no solution, infinitely many solutions