Answers 25-26 Summer - Humble ISD CR - Algebra 1 A - 2nd Nine WeeksUnit Test

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

(–6, 3)

(0, 3)

(1, –5)

(15, –1)

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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.

2 loaves of bread and 4 batches of muffins

3 loaves of bread and 3 batches of muffins

4 loaves of bread and 2 batches of muffins

5 loaves of bread and 1 batch of muffins

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

The cost of a parking permit consists of a one-time administration fee plus a monthly fee. A permit purchased for 12 months costs $660. A permit purchased for 15 months costs $810.What is the administration fee?

$50

$54

$55

$60

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

(3, 5)

(6, 2)

(8, –1)

(14, –18)

The graph represents this system of equations.

(–4, 1)

(–2, 1)

(1, –4)

(1, –2)

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?

The test contains 4 three-point questions and 20 five-point questions.

The test contains 10 three-point questions and 14 five-point questions.

The test contains 14 three-point questions and 10 five-point questions.

The test contains 20 three-point questions and 8 five-point questions.

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

(0.4, 1)

(0.8, 1)

(1, 0.4)

(1, 0.8)

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).

(5, 0)

(0, 5)

(0, –5)

(–5, 0)

Shirabi spent $208 on a sewing machine to make purses. She spends a total of $10 on thread, fabric, and accessories for each purse and plans to charge $36 for each purse. The equation represents her break-even point, when x represents the number of purses sold.208 + 10x = 36xHow many purses must she sell in order to break even?

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).

(–2.7, 2.1)

(–2.1, 2.7)

(2.1, 2.7)

(2.7, 2.1)

Erik rode down an escalator, while Raj rode up.

Erik and Raj were at the same elevation after both of them had been riding the escalator for 6 seconds.

Erik and Raj were at the same elevation after both of them had been riding the escalator for 8 seconds.

Erik and Raj were at the same elevation after Erik had been riding the escalator for 6 seconds and Raj had been on the escalator for 8 seconds.

Erik and Raj were at the same elevation after Erik had been riding the escalator for 8 seconds and Raj had been on the escalator for 6 seconds.

The graph below represents the system of equations 3x+4y=12 and 2x-y=8.

(0, 3)

(3, 0)

(4, 0)

(0, 4)

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

-2

Option

Two linear equations are shown.

(7, 4)

(7, StartFraction 13 over 3 EndFraction)

(8, StartFraction 14 over 3 EndFraction)

(9, 7)

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?

2x – y = –4

10x – 5y = –20

7x = 39

13x = 39

y=5x – 1–15x – 3y=3

one solution: (0, –1)

one solution: (1, 4)

no solution

infinite number of solutions

Anatoliy has a combination of 104 nickels and quarters totaling $22. Which system of linear equations can be used to find the number of nickels, n, and the number of quarters, q, Anatoliy has?

n + q = 22 0.05n + 0.25q = 104

n + q = 104 5n + 25q = 22

n + q = 104 0.05n + 0.25q = 22

n + q = 22 5n + 25q = 104

Jamie and Owen joined a monthly walking challenge at their youth center. Jamie has already walked 120 minutes and plans to walk 20 minutes per day. Owen plans to walk 30 minutes per day. Let x represent the number of days and y represent the total number of minutes walked during the challenge. Which system of equations can be used to find the number of days it will take for Owen and Jamie to have walked the same number of minutes?

A system of equations. y equals 20 x plus 120. y equals 30 x.

A system of equations. y equals 20 x. y equals 30 x plus 120.

A system of equations. y equals 120 x plus 20. y equals 30 x.

A system of equations. y equals 120 x. y equals 30 x plus 20.

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

The first equation should be multiplied by 2 and the second equation by 3.

The first equation should be multiplied by 2 and the second equation by −3.

The first equation should be multiplied by 3 and the second equation by 4.

The first equation should be multiplied by 3 and the second equation by −4.

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

(4, 6)

(6, 4)

(5, −1)

(−1, 5)

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

–8

–3

A graphics company charges $50 per hour to create a logo plus $250 for the ownership rights of the logo. A private contractor charges $75 per hour to develop a logo plus a $100 supply fee.Which equation can be solved to determine x, the number of hours after which the costs would be the same?

50x + 250 = 75x + 100

50 + 250x = 75 + 100x

50x + 100 = 75x + 250

50 + 100x = 75 + 250x

A pilot flew a 400-mile flight in 2.5 hours flying into the wind. Flying the same rate and with the same wind speed, the return trip took only 2 hours, with a tailwind.What was the speed of the wind?

160

180

The sum of two numbers is 28. The first number, x, is three times the second number, y.

A system of equations. x plus y equals 28. x equals 3 plus y.

A system of equations. x y equals 28. x equals 3 y.

A system of equations. x y equals 28. x equals 3 plus y.

A system of equations. x plus y equals 28. x equals 3 y.

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