Unit Test — Unit test Answers

Gillian purchased 25 books at the library book sale. Each hardcover book cost $1.50, and each paperback book cost $0.50. Gillian spent a total of $26.50. The book costs can be represented by the system of equations below. h + p = 251.50h + 0.50p = 26.50

What is the solution to the system of equations?y = –5x + 3y = 1

To eliminate the y terms and solve for x in the fewest steps, by which constants should the equations be multiplied by before adding the equations together?First equation: 4x − 3y = 34Second equation: 3x + 2y = 17

What is the solution to this system of linear equations?3x – 2y = 14 5x + y = 32

A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation.x + y = 243x + 5y = 100What does the solution of this system indicate about the questions on the test?

y=5x – 1–15x – 3y=3

Which value of m will create a system of parallel lines with no solution?y=mx-68x-4y=12

What is the solution to this system of linear equations?7x – 2y = –68x + y = 3

A coordinate grid with 2 lines. The first line passes through (0, negative 5) and (negative 5, 0). The second line passes through (0, negative 5) and (negative 2, 1).

What is the value of y in the solution to the system of equations?x + y = 12x – 3y = –30

Two linear equations are shown.

The system of equations can be solved using linear combination to eliminate one of the variables.2x − y = −4→10x − 5y = −203x + 5y = 59→3x + 5y = 59 13x = 39Which equation can replace 3x + 5y = 59 in the original system and still produce the same solution?

Helena needs 3.5 cups of flour per loaf of bread and 2.5 cups of flour per batch of muffins. She also needs 0.75 cup of sugar per loaf of bread and 0.75 cup of sugar per batch of muffins. Helena has 17 cups of flour and 4.5 cups of sugar available for baking.

What is the solution to this system of linear equations?x + y = 4x − y = 6

A coordinate grid with 2 lines. The first line is labeled y equals 0.5 x plus 3.5 and passes through (negative 3, 1), (negative 2.7, 2.1), and (0, 3.5). The second line is labeled y equals negative StartFraction 2 over 3 EndFraction x plus StartFraction 1 over 3 EndFraction and passes through the points (negative 4, 3), (negative 2.7, 2.1), and (StartFraction 1 over 3 EndFraction, 0).

What is the solution to the system of equations?y = x + 3x = –2

Casey is deciding which of two landscapers to hire. Each landscaper charges an hourly rate plus a fee for each job.Casey correctly wrote and solved a system of linear equations by substitution. In his work, he substituted an expression for one variable and solved for the other. This resulted in the equation 5 = 20. What can Casey conclude?

What value of b will cause the system to have an infinite number of solutions?

The solution to the system of equation below is (−2, −1).2x − 3y = −1 11x − 9y = −13When the first equation is multiplied by −3, the sum of the two equations is equivalent to 5x = −10.

Melinda and Paula shovel driveways and sidewalks in the winter as a way to earn extra money. Together they shoveled 450 square feet of sidewalk in 30 minutes. Then Melinda shoveled for 20 minutes while Paula shoveled for 25 minutes to complete 345 square feet of driveway.30x + 30y = 45020x + 25y = 345