Systems of Equations Practice Problems

A rectangle has a perimeter of 74 centimeters. The length of the rectangle is 5 centimeters less than twice the width. What is the area of the rectangle, in square centimeters?

• 294

• 322

• 336

• 368

Caroline and David both pay for cell phone service. Caroline uses Cell Phone Company A, which charges a monthly fee of $10 and $0.25 per minute. David uses Cell Phone Company B, which charges a monthly fee of $5 and $0.50 per minute. One month, Caroline and David both are charged the same amount. How many minutes did Caroline use?

Mathematical Equivalence

ON

Mrs. Adams bought cans of pears and cans of mixed fruit.

She bought a total of 7 cans at a cost of $21.50.

Each can of pears cost $3.20, and each can of mixed fruit cost $2.90.

How many cans of mixed fruit did Mrs. Adams purchase?

Mathematical Equivalence

ON

The length of a rectangle is three times longer than the width. The perimeter of the rectangle is 40 inches. What is the length of the rectangle in inches?

• 5

• 10

• 15

• 30

Sam traveled 20 miles in 3 hours.

Sam walked part of the distance at a speed of 4 miles per hour.

Sam rode his bicycle for the remaining distance at a speed of 12 miles per hour.

How many hours did Sam spend walking?

Mathematical Equivalence

ON

What is the x-coordinate of the solution to this system of equations?

0.1x+0.5y=0.6

0.4x−1.2y=−5.6

Mathematical Equivalence

ON

A system of two linear equations is shown on the coordinate plane.

Which of the following is the BEST estimate for the x-coordinate of the solution to this system?

• −1.8−1.8

• −0.8−0.8

• 4.5

• 5.5

Brenda had a total of $7,350 invested in two accounts. The first account earned 6% simple interest. The second account earned 10% simple interest. At the end of the year, the two accounts had earned Brenda a total of $555 in interest. The graph shows this relationship.

x = Amount invested at 6% y = Amount invested at 10%

Based on the graph, about how much was invested at each rate?

• About $3,000 was invested at 6% and $4,500 at 10%.

• About $4,500 was invested at 6% and $3,000 at 10%.

• About $7,300 was invested at 6% and $7,300 at 10%.

• About $9,300 was invested at 6% and $5,500 at 10%.

At an airport restaurant, 2 sodas and 4 hamburgers cost $12.00. An order of 4 sodas and 2 hamburgers costs $9.00. How much does one hamburger cost?

• $1.00

• $2.00

• $2.50

• $3.00

Tom wants to compare two different plans for gym membership. The first plan charges a sign-up fee of $25.00, then $5.00 for every visit. The second plan charges $100.00 per month with no sign-up fee. Tom creates a graph to find the solution to this pair of equations.

Which statement MOST accurately compares the two plans?

• If Tom plans to go to the gym 14 or fewer times during the month, he will pay less with the second plan.

• If Tom plans to go to the gym 14 or fewer times during the month, he will pay less with the first plan.

• If Tom plans to go to the gym 14 or more times during the month, he will pay less with the second plan.

• If Tom plans to go to the gym 14 or more times during the month, he will pay less with the first plan.