Solving Systems of Linear Equations

The video tutorial covers systems of equations, explaining how to solve them by graphing. It demonstrates graphing two equations, finding their intersection point, and verifying the solution. The tutorial also includes a word problem involving minigolf costs, showing how to use systems of equations to determine cost-effectiveness. It concludes with an analysis of different types of solutions, such as unique, parallel, and infinite solutions.

What does a system of equations consist of?

• One equation

• Two or more equations

• Only linear equations

• Only quadratic equations

What is the y-intercept of the first equation graphed in green?

• 3

• -3

• -1/2

• 1/2

What is the slope of the second equation graphed in pink?

• 1/2

• -1/2

• -2

• 2

Where do the two lines intersect?

• (-4, 1)

• (4, 1)

• (-4, -1)

• (4, -1)

What is the result when you plug x = 4 and y = -1 into the first equation?

• 2

• 0

• -1

• 1

In function notation, what does f(x) represent?

• The same as x

• The slope

• The y-intercept

• The same as y

How much does a non-member pay for 7 games of minigolf?

• $56

• $14

• $42

• $28

At what point does it become cheaper to be a member rather than a non-member?

• After 5 games

• After 6 games

• After 8 games

• After 7 games

What happens when two lines in a system have the same slope but different y-intercepts?

• They intersect at multiple points

• They are the same line

• They are parallel and never intersect

• They intersect at one point

What does it mean if two lines in a system are identical?

• They have infinitely many solutions

• They intersect at one point

• They are parallel

• They have no solution