End-of-Unit Assessment

Select all equations that are equivalent to $\frac{(5x+6)}2=3-(4x+12)$.

A phone company charges a base fee of $12 per month plus an additional charge per minute. The monthly phone cost $C$ can be represented by this equation: $C=12+a \boldcdot m$, where $a$ is the additional charge per minute, and $m$ is the number of minutes used.

Which equation can be used to find the number of minutes a customer used if we know $a$ and $C$?

Tickets to the zoo cost $12 for adults and $8 for children. The school has a budget of $240 for the field trip. An equation representing the budget for the trip is $240=12x+8y$. Here is a graph of this equation.

Graph of a line. Horizontal axis from 0 to 32, by 2's, number of adults. Vertical axis from 0 to 32, by 2's, number of children. Line begins on the y axis at 30, goes through 4 comma 24, 12 comma 12, and ends on the x axis at 20.

Select all the true statements.

A pizza shop sells pizzas that are 10 inches (in diameter) or larger. A 10-inch cheese pizza costs $8. Each additional inch costs $1.50, and each additional topping costs $0.75.

Write an equation that represents the cost of a pizza. Be sure to specify what the variables represent.

Consider this system of equations: $\displaystyle \begin {cases} y = \text{-}\frac{1}{2}x + 5 \\ 6x - 7y = 22 \end{cases}$ Solve the system by graphing. Label each graph and the solution.

Solve the system of equations without graphing. Show your reasoning. $\displaystyle \begin{cases} 2y=x-4 \\ 4x+3y=5 \end{cases}$

The system of equations $\begin{cases} 4x+6y=24\\ 2x+y=8 \end{cases}$ has exactly one $(x,y)$ pair for its solution.

1. If we double each side of the second equation, $2x+y=8$, we have $4x+2y=16$. Explain why the same $(x,y)$ pair that is the solution to the system is also a solution to this new equation.

2. If we add the two equations in the original system, we have $6x +7y=32$. Explain why the same $(x,y)$ pair is also a solution to this equation.