Q: A standardized test has 125 questions worth a total of 1300 points. True/False questions are worth 8 points each, and Multiple Choice questions are worth 10 points each. If $T$ is the number of True/False questions and $M$ is the number of Multiple Choice questions, which system models the situation?

$\begin{cases} T + M = 125 \\ 8T + 10M = 1300 \end{cases}$

Q: If the solution to a system of equations is $(x, y) = (2, 5)$, which of the following systems could produce this solution?

$\begin{cases} x + y = 7 \\ x - y = -3 \end{cases}$

Q: Which scenario best describes a system with exactly one solution?

Two lines that intersect at one point.

Question 1

Given the piecewise function $f(x) = \begin{cases} 2x+4 & x < 2 \ 3x-2 & x \geq 2 \end{cases}$, what is the value of $f(2)$?

Question 2

A car rental agency charges $40/day plus $0.18/mile$ for one company and $50/day plus $0.15/mile$ for another. If you plan to rent for one day, how many miles must you drive for the cost to be the same?

Accepted Answer

$333.33$ miles

Question 3

Which of the following systems of equations has no solution?

Accepted Answer

$y = 2x + 1$ and $y = 2x - 3$

Question 4

If two lines in a system of equations are parallel but not the same, what can you conclude about the system?

Accepted Answer

There is no solution.

Question 5

Given the system $\begin{cases} 2x + y = 6 \ x - y = 4 \end{cases}$, what is the solution $(x, y)$?

Accepted Answer

$(\boxed{4, 0})$

Question 6

A standardized test has 125 questions worth a total of 1300 points. True/False questions are worth 8 points each, and Multiple Choice questions are worth 10 points each. If $T$ is the number of True/False questions and $M$ is the number of Multiple Choice questions, which system models the situation?

Accepted Answer

$\begin{cases} T + M = 125 \ 8T + 10M = 1300 \end{cases}$

Question 7

What is the break-even point for the revenue function $R(x) = 0.85x$ and the cost function $C(x) = 1.1x + 35$?

Accepted Answer

$x = 140$

Question 8

Which method is most efficient for solving a system of equations when one variable can be easily isolated?

Accepted Answer

Substitution

Question 9

If a system of equations has infinitely many solutions, what does this mean about the graphs of the equations?

Accepted Answer

The lines are the same.

Question 10

Given the system $\begin{cases} 3x - y = 7 \ 2x + y = 8 \end{cases}$, what is the value of $x$?

Accepted Answer

$x = 4$

Question 11

A rectangular metal sheet is 8 feet longer than it is wide. If the perimeter is 228 feet, what is the width?

Accepted Answer

$58$ feet

Question 12

Which of the following systems has infinitely many solutions?

Accepted Answer

$y = 2x + 3$ and $2y = 4x + 6$

Question 13

If you solve the system $\begin{cases} x + y = 5 \ x - y = 1 \end{cases}$ by elimination, what is the value of $y$?

Accepted Answer

$y = 3$

Question 14

Which of the following is NOT a valid method for solving a system of linear equations?

Accepted Answer

Factoring

Question 15

A system of equations is given by $\begin{cases} 4x + 2y = 6 \ 2x + y = 3 \end{cases}$. What is the relationship between the two equations?

Accepted Answer

They are the same line.

Question 16

If the solution to a system of equations is $(x, y) = (2, 5)$, which of the following systems could produce this solution?

Accepted Answer

$\begin{cases} x + y = 7 \ x - y = -3 \end{cases}$

Question 17

Which scenario best describes a system with exactly one solution?

Accepted Answer

Two lines that intersect at one point.

Question 18

If you graph the equations $y = 2x + 3$ and $y = -x + 1$, what is the solution to the system?

Accepted Answer

$(x, y) = (-2/3, 5/3)$

Question 19

Which of the following is the correct piecewise equation for the graph below, where the slope changes at $x = 2$?

Accepted Answer

$f(x) = \begin{cases} 2x+4 & x < 2 \ 3x-2 & x \geq 2 \end{cases}$

B5

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