Exploring Systems of Equations through Graphing Word Problems

This video tutorial covers systems of equations, focusing on points of intersection as solutions. It provides examples of solving systems of equations and includes a word problem involving skittles. The tutorial demonstrates how to graph equations to find solutions, emphasizing the importance of understanding intersections in systems of equations.

What is a system of equations?

• A single equation with multiple variables

• Two or more equations that are solved together

• An equation with no variables

• A graph with no intersections

What is the point where two lines intersect called?

• Vertex

• Midpoint

• Point of intersection

• Origin

What does the point of intersection represent in a system of equations?

• The midpoint of the lines

• The solution to the system

• The starting point of the graph

• The highest point on the graph

In the example given, what are the coordinates of the point of intersection?

• (1, 1)

• (4, 4)

• (2, 2)

• (3, 3)

What is the equation for Aaron's skittles consumption?

• y = 30 + 4x

• y = 30 - 4x

• y = 20 - 2x

• y = 20 + 2x

What is the equation for Randall's skittles consumption?

• y = 20 + 2x

• y = 20 - 2x

• y = 30 + 4x

• y = 30 - 4x

What is the y-intercept of Aaron's equation?

• 10

• 20

• 30

• 40

What is the slope of Randall's equation?

• 4

• -4

• -2

• 2

At what point do Aaron and Randall have the same number of skittles?

• (4, 5)

• (7, 20)

• (5, 10)

• (6, 15)

What does the point (5, 10) represent in the context of the story problem?

• After 5 minutes, Aaron and Randall have 10 skittles each

• Aaron and Randall start with 10 skittles each

• After 10 minutes, Aaron and Randall have 5 skittles each

• Aaron and Randall start with 5 skittles each