Question 1

work. Do not solve.
-5x + 9y = -12
-4x - 4y = -32

Accepted Answer

First, we can set up a system of equations: 
q + h = 17 (since Andy has 17 coins total) 
0.25q + 0.5h = 5.25 (since the total value of the coins is $5.25) 
We can then use elimination to solve for q:

- Multiply the second equation by 4 to get rid of the decimals: 
q + 2h = 21 
q + 2h = 21 
- Subtract the first equation from the second: 
0 = 4 
This is not true, meaning there is no solution. However, we made a mistake along the way. Let's go back to the original equations and try again:

q + h = 17 
0.25q + 0.5h = 5.25

- Multiply the first equation by 0.25: 
0.25q + 0.25h = 4.25 
0.25q + 0.5h = 5.25 
- Subtract the first equation from the second: 
0.25h = 1 
h = 4 
- Plug h back into the first equation to find q: 
q + 4 = 17 
q = 13

Therefore, Andy has 13 quarters.

Question 2

Write the word or phrase that best completes each statement or answers the question.
-A store sells televisions for $360 and digital video recorders for $270. At the beginning of the week its entire stock is worth $59,580. During the week it sells three quarters of the televisions and one
Third of the digital video recorders for a total of $34,560. How many televisions and digital video
Recorders did it have in its stock at the beginning of the week?

Accepted Answer

Let the number of televisions be $T$ and the number of digital video recorders be $D$. The total value of the stock is given by $360T + 270D = 59580$. The value of the items sold is $34,560$, which comes from selling $3/4$ of the televisions and $1/3$ of the digital video recorders, so the equation for the sales is $270(360T(3/4) + 270D(1/3)) = 34560$. Solving these equations simultaneously gives $T = 98$ and $D = 90$, making option B correct.

Question 3

Write the word or phrase that best completes each statement or answers the question.
-South Wind Vineyards uses 830 acres to plant Chardonnay and Riesling grapes. The vintner knows the profits will be greatest by planting 240 more acres of Chardonnay than Riesling. How
Many acres of each grape should be planted?

Accepted Answer

Let's assume that Riesling will be planted on x acres. According to the problem, Chardonnay will be planted on 240 more acres than Riesling, which means it will be planted on (x + 240) acres. The total planted area is given as 830 acres, so we can write an equation: x + (x + 240) = 830
This simplifies to 2x = 590, and x = 295. Therefore, Riesling will be planted on 295 acres and Chardonnay on (295 + 240) = 535 acres. So, the best choice is B.

Question 4

work. Do not solve.
-5x + 9y = -12
-4x - 4y = -32
A) Substitution B) Addition
Answer: B
Write the word or phrase that best completes each statement or answers the question.
-Write a system of equations that would be more easily solved using the substitution
method than the addition method. Explain why substitution would be easier than
addition.

Accepted Answer

The answer of work. Do not solve.
-5x + 9y =...

Question 5

Write the word or phrase that best completes each statement or answers the question.
-Adam has a total of 62 coins, all of which are either dimes or nickels. The total value of the coins is $5.35. Find the number of each type of coin.

Accepted Answer

Let the number of nickels be $n$ and the number of dimes be $d$. We have two equations: $n + d = 62$ and $0.05n + 0.10d = 5.35$. Solving these equations simultaneously, we find $n = 17$ and $d = 45$.

Question 6

work. Do not solve.
-5x + 9y = -12
-4x - 4y = -32
A) Substitution B) Addition
Answer: B
Write the word or phrase that best completes each statement or answers the question.
-A student tried to clear the fractions in $$\begin{array} { l } 
\frac { x } { 2 } + \frac { y } { 7 } = - 2 \
\frac { x } { 6 } + \frac { y } { 3 } = 1
\end{array}$$

Accepted Answer

The answer of work. Do not solve.
-5x + 9y =...

Question 7

Write the word or phrase that best completes each statement or answers the question.
-There were 35,000 people at a ball game in Los Angeles. The dayʹs receipts were $238,000. How many people paid $12 for reserved seats and how many paid $5 for general admission?

Accepted Answer

The answer of Write the word or phrase that best...

Question 8

Write the word or phrase that best completes each statement or answers the question.
-$$\begin{array} { l } 
\frac { 1 } { 5 } x - \frac { 1 } { 4 } y = 3 \
\frac { 2 } { 5 } x + \frac { 1 } { 2 } y = 2
\end{array}$$

Accepted Answer

To solve the system of equations, we can use either substitution or elimination method. Here, using the elimination method seems efficient. We can multiply the first equation by 2 and the second equation by -1 to eliminate $y$ when we add them together:$$2\left( \frac{1}{5}x - \frac{1}{4}y \right) = 2(3)$$$$-1\left( \frac{2}{5}x + \frac{1}{2}y \right) = -1(2)$$This simplifies to:$$\frac{2}{5}x - \frac{1}{2}y = 6$$$$-\frac{2}{5}x - \frac{1}{2}y = -2$$Adding these equations, we eliminate $y$, and we are left with:$$0x - y = 4$$This simplification was incorrect; let's correct the approach:First, we align the equations for clarity:$$\frac{1}{5}x - \frac{1}{4}y = 3 \quad \text{(1)}$$$$\frac{2}{5}x + \frac{1}{2}y = 2 \quad \text{(2)}$$To eliminate $y$, we can multiply (1) by 2 and (2) by -1 (to get common coefficients for $y$):$$2\left(\frac{1}{5}x - \frac{1}{4}y\right) = 2(3)$$$$-1\left(\frac{2}{5}x + \frac{1}{2}y\right) = -1(2)$$This gives us:$$\frac{2}{5}x - \frac{1}{2}y = 6$$$$-\frac{2}{5}x - \frac{1}{2}y = -2$$The mistake was in the calculation and the approach to eliminate $y$. To correctly solve the system, let's directly solve the original system without the incorrect step:Multiply the first equation by 4 and the second by 5 to eliminate $y$:$$4\left(\frac{1}{5}x - \frac{1}{4}y\right) = 4(3)$$$$5\left(\frac{2}{5}x + \frac{1}{2}y\right) = 5(2)$$This simplifies to:$$\frac{4}{5}x - y = 12$$$$2x + \frac{5}{2}y = 10$$The correct approach involves finding a common coefficient for either $x$ or $y$ in both equations and then adding or subtracting the equations to find the value of one variable. Then, substitute back to find the other variable. The mistake in the simplification process led to confusion. To find the correct solution, one should correctly apply the elimination or substitution method without the simplification error. Given the options and recognizing the mistake in the process, the correct solution involves accurately solving the system, which might lead to finding that the coordinates $(10, -4)$ satisfy both equations when the correct arithmetic is applied.

Question 9

Write the word or phrase that best completes each statement or answers the question.
-$\frac { 1 } { 4 } x + \frac { 1 } { 4 } y = 0$ $x - y = - 4$

Accepted Answer

First, we can rearrange the first equation to get:
$$\frac{1}{4}x=-\frac{1}{4}y$$
$$x=-y$$
Substituting this into the second equation, we get:
$$-y-y=-4$$
$$y=2$$
Substituting this back into either equation, we get:
$$x=-y=-2$$
Therefore, the solution is $(x,y)=(-2,2)$ which corresponds to choice C.

Question 10

Write the word or phrase that best completes each statement or answers the question.
-A vendor sells hot dogs and bags of potato chips. A customer buys 4 hot dogs and 5 bags of potato chips for $16.75. Another customer buys 2 hot dogs and 3 bags of potato chips for $9.25. Find the
Cost of each item.

Accepted Answer

By setting up a system of equations based on the given information and solving, we find that hot dogs cost $2.00 each and bags of potato chips cost $1.75 each.

Question 11

work. Do not solve.
-5x + 9y = -12
-4x - 4y = -32
A) Substitution B) Addition
Answer: B
Write the word or phrase that best completes each statement or answers the question.
-While using the addition method, if the following occurs, what can you say about the
graph of the system of equations?
3x - 7y = 8
- 3x + 7y = -8
0 = 0

Accepted Answer

The answer of work. Do not solve.
-5x + 9y =...

Question 12

work. Do not solve.
-5x + 9y = -12
-4x - 4y = -32
A) Substitution B) Addition
Answer: B
Write the word or phrase that best completes each statement or answers the question.
-Explain how the multiplication and addition principles are used in solving systems of
equations using the addition method.

Accepted Answer

The answer of work. Do not solve.
-5x + 9y =...

Question 13

Write the word or phrase that best completes each statement or answers the question.
-$$\begin{array} { l } 
2 x + 3 y = 5 \
6 x = 10 + 9 y
\end{array}$$

Accepted Answer

Rearranging the first equation, we get $y=\frac{5-2x}{3}$. Substituting this into the second equation, we get $6x=10+9\left(\frac{5-2x}{3}ight)$. Solving for $x$, we get $x=\frac{25}{18}$. Substituting this back into the first equation and solving for $y$, we get $y=\frac{5}{18}$. Therefore, the solution is $\boxed{	extbf{(C) } \left(\frac{25}{12},\frac{5}{18}ight)}$.

Question 14

work. Do not solve.
-5x + 9y = -12
-4x - 4y = -32

Accepted Answer

The answer of work. Do not solve.
-5x + 9y =...

Question 15

Write the word or phrase that best completes each statement or answers the question.
-$\text { [ohn has a jarful of quarters and nickels. There are }$

Accepted Answer

The number of quarters and nickels in the jar add up to 96. This eliminates choices A and B, which have too many quarters. Choice D has too many quarters as well. Therefore, choice C is the best option as it has 40 quarters and 56 nickels, which add up to a total of 96 coins.

Question 16

Write the word or phrase that best completes each statement or answers the question.
-$$\frac { 1 } { 4 } x + \frac { 1 } { 4 } y = 0$$
$\frac { 1 } { 4 } x - \frac { 1 } { 4 } y = - \frac { 7 } { 2 }$

Accepted Answer

The answer of Write the word or phrase that best...

Question 17

work. Do not solve.
-5x + 9y = -12
-4x - 4y = -32

Accepted Answer

The system of equations can be solved by addition (or elimination) method by multiplying one or both equations to make the coefficients of one of the variables opposite, then adding the equations to eliminate that variable.DLet x be the number of one-dollar bills and y be the number of five-dollar bills. The system of equations would be x + y = 74 (total bills) and x + 5y = 278 (total amount). Solving this system, you find that x, the number of one-dollar bills, is 51.

Question 18

work. Do not solve.
-5x + 9y = -12
-4x - 4y = -32
A) Substitution B) Addition
Answer: B
Write the word or phrase that best completes each statement or answers the question.
-Write a system of equations that would be more easily solved using the addition method
than the substitution method. Explain why addition would be easier than substitution.

Accepted Answer

The answer of work. Do not solve.
-5x + 9y =...

Question 19

work. Do not solve.
-5x + 9y = -12
-4x - 4y = -32
A) Substitution B) Addition
Answer: B
Write the word or phrase that best completes each statement or answers the question.
--4x + 5y = A
4x - 3y = B
For what values of A or B can this system of equations have (0, 0) as a solution?

Accepted Answer

The answer of work. Do not solve.
-5x + 9y =...

Question 20

work. Do not solve.
-5x + 9y = -12
-4x - 4y = -32
A) Substitution B) Addition
Answer: B
Write the word or phrase that best completes each statement or answers the question.
-2x + 3y = -1
4x + 2y = -3
What number would you multiply the top equation by to eliminate the x terms?

Accepted Answer

The answer of work. Do not solve.
-5x + 9y =...

Quiz 4: Systems of Equations

work. Do not solve. -5x + 9y = -12 -4x - 4y = -32 A) Substitution B) Addition Answer: B Write the word or phrase that best completes each statement or answers the question. -Andy has 17 coins made up of quarters and half dollars, and their total value is $5.25. How many quarters does he have?

Write the word or phrase that best completes each statement or answers the question. -Adam has a total of 62 coins, all of which are either dimes or nickels. The total value of the coins is $5.35. Find the number of each type of coin.

Write the word or phrase that best completes each statement or answers the question. -There were 35,000 people at a ball game in Los Angeles. The dayʹs receipts were $238,000. How many people paid $12 for reserved seats and how many paid $5 for general admission?

Write the word or phrase that best completes each statement or answers the question. - $\begin{array} { l } \frac { 1 } { 5 } x - \frac { 1 } { 4 } y = 3 \\\frac { 2 } { 5 } x + \frac { 1 } { 2 } y = 2\end{array}$

Write the word or phrase that best completes each statement or answers the question. - $\frac { 1 } { 4 } x + \frac { 1 } { 4 } y = 0$ $x - y = - 4$

Write the word or phrase that best completes each statement or answers the question. -A vendor sells hot dogs and bags of potato chips. A customer buys 4 hot dogs and 5 bags of potato chips for $16.75. Another customer buys 2 hot dogs and 3 bags of potato chips for $9.25. Find the Cost of each item.

work. Do not solve. -5x + 9y = -12 -4x - 4y = -32 A) Substitution B) Addition Answer: B Write the word or phrase that best completes each statement or answers the question. -Explain how the multiplication and addition principles are used in solving systems of equations using the addition method.

Write the word or phrase that best completes each statement or answers the question. - $\begin{array} { l } 2 x + 3 y = 5 \\6 x = 10 + 9 y\end{array}$

work. Do not solve. -5x + 9y = -12 -4x - 4y = -32 A) Substitution B) Addition Answer: B Write the word or phrase that best completes each statement or answers the question. -A sum of money amounting to $3.10 consists of dimes and quarters. If there are 16 coins in all, how many are quarters?

Write the word or phrase that best completes each statement or answers the question. - $\text { [ohn has a jarful of quarters and nickels. There are }$

Write the word or phrase that best completes each statement or answers the question. - $\frac { 1 } { 4 } x + \frac { 1 } { 4 } y = 0$ $\frac { 1 } { 4 } x - \frac { 1 } { 4 } y = - \frac { 7 } { 2 }$

work. Do not solve. -5x + 9y = -12 -4x - 4y = -32 A) Substitution B) Addition Answer: B Write the word or phrase that best completes each statement or answers the question. --4x + 5y = A 4x - 3y = B For what values of A or B can this system of equations have (0, 0) as a solution?

work. Do not solve. -5x + 9y = -12 -4x - 4y = -32 A) Substitution B) Addition Answer: B Write the word or phrase that best completes each statement or answers the question. -2x + 3y = -1 4x + 2y = -3 What number would you multiply the top equation by to eliminate the x terms?

Quiz 4: Systems of Equations

work. Do not solve. -5x + 9y = -12 -4x - 4y = -32 A) Substitution B) Addition Answer: B Write the word or phrase that best completes each statement or answers the question. -Andy has 17 coins made up of quarters and half dollars, and their total value is $5.25. How many quarters does he have?

Write the word or phrase that best completes each statement or answers the question. -Adam has a total of 62 coins, all of which are either dimes or nickels. The total value of the coins is $5.35. Find the number of each type of coin.

Write the word or phrase that best completes each statement or answers the question. -There were 35,000 people at a ball game in Los Angeles. The dayʹs receipts were $238,000. How many people paid $12 for reserved seats and how many paid $5 for general admission?

Write the word or phrase that best completes each statement or answers the question. - 15x−14y=325x+12y=2\begin{array} { l } \frac { 1 } { 5 } x - \frac { 1 } { 4 } y = 3 \\\frac { 2 } { 5 } x + \frac { 1 } { 2 } y = 2\end{array}51​x−41​y=352​x+21​y=2​

Write the word or phrase that best completes each statement or answers the question. - 14x+14y=0\frac { 1 } { 4 } x + \frac { 1 } { 4 } y = 041​x+41​y=0 x−y=−4x - y = - 4x−y=−4

work. Do not solve. -5x + 9y = -12 -4x - 4y = -32 A) Substitution B) Addition Answer: B Write the word or phrase that best completes each statement or answers the question. -Explain how the multiplication and addition principles are used in solving systems of equations using the addition method.

Write the word or phrase that best completes each statement or answers the question. - 2x+3y=56x=10+9y\begin{array} { l } 2 x + 3 y = 5 \\6 x = 10 + 9 y\end{array}2x+3y=56x=10+9y​

work. Do not solve. -5x + 9y = -12 -4x - 4y = -32 A) Substitution B) Addition Answer: B Write the word or phrase that best completes each statement or answers the question. -A sum of money amounting to $3.10 consists of dimes and quarters. If there are 16 coins in all, how many are quarters?

Write the word or phrase that best completes each statement or answers the question. - [ohn has a jarful of quarters and nickels. There are \text { [ohn has a jarful of quarters and nickels. There are } [ohn has a jarful of quarters and nickels. There are

Write the word or phrase that best completes each statement or answers the question. - 14x+14y=0\frac { 1 } { 4 } x + \frac { 1 } { 4 } y = 041​x+41​y=0 14x−14y=−72\frac { 1 } { 4 } x - \frac { 1 } { 4 } y = - \frac { 7 } { 2 }41​x−41​y=−27​

work. Do not solve. -5x + 9y = -12 -4x - 4y = -32 A) Substitution B) Addition Answer: B Write the word or phrase that best completes each statement or answers the question. --4x + 5y = A 4x - 3y = B For what values of A or B can this system of equations have (0, 0) as a solution?

work. Do not solve. -5x + 9y = -12 -4x - 4y = -32 A) Substitution B) Addition Answer: B Write the word or phrase that best completes each statement or answers the question. -2x + 3y = -1 4x + 2y = -3 What number would you multiply the top equation by to eliminate the x terms?

Write the word or phrase that best completes each statement or answers the question. - $\begin{array} { l } \frac { 1 } { 5 } x - \frac { 1 } { 4 } y = 3 \\\frac { 2 } { 5 } x + \frac { 1 } { 2 } y = 2\end{array}$

Write the word or phrase that best completes each statement or answers the question. - $\frac { 1 } { 4 } x + \frac { 1 } { 4 } y = 0$ $x - y = - 4$

Write the word or phrase that best completes each statement or answers the question. - $\begin{array} { l } 2 x + 3 y = 5 \\6 x = 10 + 9 y\end{array}$

Write the word or phrase that best completes each statement or answers the question. - $\text { [ohn has a jarful of quarters and nickels. There are }$

Write the word or phrase that best completes each statement or answers the question. - $\frac { 1 } { 4 } x + \frac { 1 } { 4 } y = 0$ $\frac { 1 } { 4 } x - \frac { 1 } { 4 } y = - \frac { 7 } { 2 }$