Answers PARTA - EOP PGCPS ALGEBRA 1 CR FALL2026 - 793023Solving Systems: Introduction to Linear Combinations

Solving Systems: Introduction to Linear Combinations — Test Answers

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Tickets to a basketball game can be ordered online for a set price per ticket plus a $5.50 service fee. The total cost in dollars for ordering 5 tickets is $108.00. Which linear function represents c, the total cost, when x tickets are ordered? (A service fee is a single fee applied to the total, no matter the number of tickets purchased).

c(x) = 5.50 + 20.50x

c(x) = 5.50x + 20.50

c(x) = 5.50 + 21.60x

c(x) = 5.50x + 21.60

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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.

Two linear equations are shown.

(7, 4)

(7, StartFraction 13 over 3 EndFraction)

(8, StartFraction 14 over 3 EndFraction)

(9, 7)

Which graph shows a set of ordered pairs that represent a function?

Option

A coordinate plane from negative 8 to 8 along the x-axis and from negative 7 to 7 along the y-axis.

1. Plot the point (2, 4).2. From that point, count left 3 units and down 1 unit and plot a second point. 3. Draw a line through the two points.

1. Plot the point (2, 4).2. From that point, count left 1 unit and down 3 units and plot a second point. 3. Draw a line through the two points.

1. Plot the point (–2,4).2. From that point, count left 3 units and down 1 unit and plot a second point. 3. Draw a line through the two points.

1. Plot the point (–2,4).2. From that point, count left 1 unit and down 3 units and plot a second point. 3. Draw a line through the two points.

The graph represents a functional relationship.

–14

–2

On a coordinate plane, a curved line with a maximum value of (negative 1, 2) crosses the x-axis at (negative 3, 0) and (1, 0), and crosses the y-axis at (0, 1.5).

(–3, 0) and (0, 1.5)

(–3, 0) and (1,0)

(–1, 2) and (1, 0)

(0, 1.5) and (1, 0)

A store offers packing and mailing services to customers. The cost of shipping a box is a combination of a flat packing fee of $5 and an amount based on the weight in pounds of the box, $2.25 per pound. Which equation represents the shipping cost as a function of x, the weight in pounds?

f(x) = 2.25x + 5

f(x) = 5x + 2.25

f(x) = 2.25x − 5

f(x) = 5x − 2.25

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)

The volume of air inside a rubber ball with radius r can be found using the function . What does represent?

the radius of the rubber ball when the volume equals cubic feet

the volume of the rubber ball when the radius equals feet

that the volume of the rubber ball is 5 cubic feet when the radius is 7 feet

that the volume of the rubber ball is 7 cubic feet when the radius is 5 feet

The table represents a linear function.

–3

–2

Pauley graphs the change in temperature of a glass of hot tea over time. He sees that the function appears to decrease quickly at first, then decrease more slowly as time passes. Which best describes this function?

It is linear because the graph decreases over time.

It is linear because there is both an independent and a dependent variable.

It is nonlinear because linear functions are increasing functions.

It is nonlinear because linear functions increase or decrease at the same rate.

A 2-column table with 6 rows. The first column is labeled x with entries negative 4, negative 2, 0, 2, 4, 6. The second column is labeled f of x with entries 0, 2, 8, 2, 0, negative 2.

(0, 8)

(–4, 0)

(–4, 0), (4, 0)

(–4, 0), (0, 8), (4, 0)

The function f(x) is shown on the graph.

12 only

2 and 3 only

–2, –1, 1, and 2 only

–2, –1, 1, 2 and 12

A store sells notebooks for $3 each and does not charge sales tax. If x represents the number of notebooks Adele buys and y represents the total cost of the notebooks she buys, which best describes the values of x and y?

The value of x can be any real number, and y will be a real number.

The value of x can be any real number greater than or equal to 0, and y will be a real number greater than or equal to 0.

The value of x can be any integer, and y will be an integer.

The value of x can be any integer greater than or equal to 0, and y will be an integer greater than or equal to 0.

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

(–6, 3)

(0, 3)

(1, –5)

(15, –1)

A 2-column table with 4 rows. The first column is labeled x with entries negative 6, negative 1, 0, 3. The second column is labeled y with entries negative 7, 1, 9, negative 2.

{x | x = –6, –1, 0, 3}

{y | y = –7, –2, 1, 9}

{x | x = –7, –6, –2, –1, 0, 1, 3, 9}

{y | y = –7, –6, –2, –1, 0, 1, 3, 9}

Which equation represents the line that passes through (–6, 7) and (–3, 6)?

y = –x + 9

y = –x + 5

y = –3x – 11y

y = –3x + 25

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Solving Systems: Introduction to Linear Combinations — Test Answers

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