Exploring Systems of Equations through Graphing

The video tutorial introduces systems of equations and demonstrates how to solve them by graphing. It covers the concept of intersecting lines as solutions and provides three detailed examples, each illustrating different methods and scenarios. The tutorial emphasizes the importance of graphing tools and accuracy. The final example is left for students to practice independently, reinforcing the learning objectives.

What is a system of equations?

• Two equations that never intersect

• Two equations that intersect at one point

• A single equation with two variables

• Two equations that are parallel

What is the solution to a system of equations?

• The point where the two lines intersect

• The point where the two lines are tangent

• The point where the two lines are parallel

• The point where the two lines diverge

In the first example, what is the equation of the orange line?

• y = 3x + 1

• y = -2x + 1

• y = 3

• y = 2/3x + 1

What is the solution to the first example?

• (2, 2)

• (2, 3)

• (3, 2)

• (3, 3)

In the second example, what is the slope of the first equation?

• 2/3

• -2

• -1/2

• 3

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

• 4

• 1

• -1

• 3

What is the solution to the second example?

• (1, -1)

• (1, 1)

• (-1, -1)

• (-1, 1)

In the third example, what is the starting point of the first equation?

• (-1, 1)

• (1, -1)

• (-2, 2)

• (2, -2)

What is the slope of the second equation in the third example?

• 1/2

• -1/2

• -2

• 2

What is the x-coordinate of the solution in the third example?

• 4

• 3

• 2

• 1