Unit 2 Learning Checkpoint 1

If a system of two linear equations has infinitely many solutions, which of the following statements describes the graph of the corresponding two lines in the xy-plane?

• The lines are coinciding.

• The lines are intersecting at only one point.

• The lines are parallel.

• The lines are perpendicular.

The table gives some values of x and their corresponding values of y for the graphs of lines ℓ and k in the xy-plane. The system of equations consisting of the equations for lines ℓ and k has solution (x,y). What is the ordered pair that is the solution of this system?

• (-1, -2)

• (0.5, 6.5)

• (1.5, 5.5)

• (3, 10)

Ally and Brett decide to go jogging along a two-mile straight path at a nearby park. Ally starts jogging before Brett does. Sometime after Ally starts jogging, Brett begins jogging from the same starting point and along the same path as Ally. Each is jogging at a constant rate. Which of the following statements about Ally’s jogging rate and Brett’s jogging rate must be true?

• If Brett’s constant rate is greater than Ally’s constant rate, he may catch up to Ally before she reaches the end of the two-mile path.

• If Brett’s constant rate is equal to Ally’s constant rate, he may catch up to Ally before she reaches the end of the two-mile path.

• If Brett’s constant rate is less than Ally’s constant rate, he may catch up to Ally before she reaches the end of the two-mile path.

• At any constant rate Brett jogs, he will not catch up to Ally before she reaches the end of the two-mile path.

• (-5, 31)

• (-4, 1)

• (-3, 5)

• (5, -19)

• It has one solution because the lines have different slopes.

• It has two solutions because there are two variables in the equations.

• It has no solution because the lines have the same slopes and different y-intercepts.

• It has infinitely many solutions because the lines have the same slopes and y-intercepts.

A local movie theater sells tickets at different prices for an adult and for a child. The price of an adult’s ticket is $10.50 and the price of a child’s ticket is $6.50. If the theater sells a total of 65 tickets for a total price of $594.50 in an afternoon, how many child tickets did the theater sell?

• 22

• 43

• 65

• 88

Brenda is solving the system of equations A, shown in the table, by using the elimination method. She produced system of equations B as her first step in the solution method. Which of the following statements justifies the two systems being equivalent?

• The sum of the two equations in system A produces the first equation in system B.

• The sum of the two equations in system A produces the second equation in system B.

• Dividing both sides of the first equation in system A by 2 produces the first equation in system B, and dividing both sides of the second equation in system A by 5 produces the second equation in system B.

• Multiplying both sides of the first equation in system A by 2 produces the first equation in system B, and multiplying both sides of the second equation in system A by 5 produces the second equation in system B.

• 30

• 8

• 2

• -2

• The graphs of the functions do not intersect because they have different y-intercepts.

• The graphs of the functions intersect at the point (-12,-29) because that is a solution to the equation g(x) = h(x).

• The graphs of the functions intersect at the point (-29,-12) because g(x) = h(x) when x =-29.