Solving Systems of Equations

Multiple Choice

Identify the choice that best completes the statement or answers the question.

        1.        Tell whether the ordered pair (5, –3) is a solution of the system .

a.

no

b.

yes

        2.        Solve the system  by graphing.

        3.        The Fun Guys game rental store charges an annual fee of $5 plus $5.50 per game rented. The Game Bank charges an annual fee of $17 plus $2.50 per game. For how many game rentals will the cost be the same at both stores? What is that cost?

a.

3 games; $22

c.

4 games; $27

b.

2 games; $16

d.

6 games; $38

        4.        If the pattern in the table continues, in what month will the number of sales of CDs and movie tickets be the same? What number will that be?

Total Number Sold

Month

1

2

3

4

CDs

700

685

670

655

Movie tickets

100

145

190

235

a.

Month 10; 550

c.

Month 9; 580

b.

Month 11; 550

d.

Month 8; 580

        5.        Solve  by using substitution. Express your answer as an ordered pair.

        6.        Solve  by using substitution. Express your answer as an ordered pair.

a.

(8, –4)

c.

(–2, 4)

b.

(4, –8)

d.

(4, 8)

        7.        Solve  by using substitution.

a.

c.

b.

d.

        8.        Solve  by using elimination. Express your answer as an ordered pair.

a.

(–2, –3)

c.

(0, –2)

b.

(–2, 0)

d.

(–8, –6)

        9.        Solve  by using elimination. Express your answer as an ordered pair.

a.

(5, 0)

c.

(5, 22.5)

b.

(5, 17.5)

d.

(5, 0)

        10.        Solve  by using elimination. Express your answer as an ordered pair.

        11.        At the local pet store, zebra fish cost $2.10 each and neon tetras cost $1.85 each. If Marsha bought 13 fish for a total cost of $25.80, not including tax, how many of each type of fish did she buy?

a.

7 zebra fish, 6 neon tetras

c.

6 zebra fish, 7 neon tetras

b.

8 zebra fish, 5 neon tetras

d.

5 zebra fish, 8 neon tetras

        12.        Solve

        13.        Solve .

a.

This system has exactly one solution.

b.

This system has infinitely many solutions.

c.

This system has no solution.

d.

(1, 1) and (0, 0)

        14.        Elena and her husband Marc both drive to work. Elena’s car has a current mileage (total distance driven) of 9,000 and she drives 18,000 miles more each year. Marc’s car has a current mileage of 60,000 and he drives 7,000 miles more each year. Will the mileages for the two cars ever be equal? Explain.

a.

No; The equations have different slopes, so the lines do not intersect.

b.

No; The equations have equal slopes but different y-intercepts, so the lines do not intersect.

c.

Yes; The equations have different y-intercepts, so the lines intersect.

d.

Yes; The equations have different slopes, so the lines intersect.

Numeric Response

        15.        What value of b will make the system  and  intersect at the point ?