Question 1

Use a table to solve the system of equations. If you use a calculator table, record the TbIStart and $\mathrm { V}_{TbI }$ entered. $$\begin{array} { r } 
x - 2 y = 7 \
2 x + 3 y = 0
\end{array}$$
A) (4, -2)
B) (3, -2)
C) (5, -2)
D) (3, -3)
E) (3, -1)

Accepted Answer

B

Question 2

Do the graphs of the equations form coincident lines? (It is not necessary to graph them.) $$\begin{array} { l } 
2 x + y = 4 \
2 y + x = 4
\end{array}$$
A) yes
B) no
C) insufficient information

Accepted Answer

We can rearrange each equation to y = -2x + 4 and y = -1/2x + 2 respectively. These are the equations of two distinct lines with different slopes, therefore they cannot be coincident.

Question 3

Use a table to solve the system of equations. If you use a calculator table, record the TbIStart and $\mathrm { V}_{TbI }$ entered. $$\begin{array} { c } 
5 x - 3 y = 11 \
- 20 x + 12 y = - 44
\end{array}$$
A) (5, -3)
B) (3, 5)
C) (-5, -4)
D) (-4, 3)
E) any (x, y) on line $5 x - 3 y = 11$

Accepted Answer

The second equation is a multiple of the first, indicating they are the same line. Thus, any (x, y) on the line $5x - 3y = 11$ is a solution.

Question 4

Do the graphs of the equations form parallel lines? (It is not necessary to graph them.) $$\begin{array} { l } 
y = 4 x \
y = \frac { 1 } { 4 } ( 12 + 20 x )
\end{array}$$
A) yes
B) no
C) insufficient information

Accepted Answer

The first equation has a slope of 4, while the second equation has a slope of 5. Therefore, the graphs of the two equations are not parallel.

Question 5

Do the graphs of the equations form coincident lines? (It is not necessary to graph them.) $$\begin{array} { l } 
y + x = 30 \
2 x = 60 - 2 y
\end{array}$$
A) yes
B) no
C) insufficient information

Accepted Answer

Rearranging the second equation, we get $y=-x+30$. This equation is the same as the first equation, so they represent coincident lines.

Question 6

Do the graphs of the equations form coincident lines? (It is not necessary to graph them.) $$\begin{array} { l } 
y = x + 0.04 x \
y = 1.04 x
\end{array}$$
A) yes
B) no
C) insufficient information

Accepted Answer

Both equations can be simplified to $y=1.04x$, which means they have the same slope and intercept. Therefore, their graphs would be coincident.

Question 7

Do the graphs of the equations form coincident lines? (It is not necessary to graph them.) $$\begin{array} { l } 
y + 100 x = 400 \
y = 100 - 400 x
\end{array}$$
A) yes
B) no
C) insufficient information

Accepted Answer

To determine if the lines are coincident, we need to check if they have the same slope and y-intercept.

The first equation can be rewritten in slope-intercept form as:

$y = -100x + 400$

Comparing this to the second equation, we can see that they do not have the same slope, since the second equation has a slope of -400. Therefore, the lines are not coincident.

Question 8

Write a system of equations to describe the problem situation. It is not necessary to solve the problem. Paolo earns $481 from working 54 total hours at two jobs. He earns $6.55 per hour (x) at the first job and $9.20 per hour (y) at the second job.
A) $x = 54 + y , 6.55 x + 9.20 y = 481$
B) $x + y = 54,9.20 x + 6.55 y = 481$
C) $x + y = 54,6.55 x + 9.20 y = 481$
D) $x + y = 54,6.55 x - 9.20 y = 481$
E) $x - y = 54,655 x + 9.20 y = 481$

Accepted Answer

We know that Paolo earns $6.55 per hour (x) at the first job and $9.20 per hour (y) at the second job. The total hours worked are 54, so we can set up two equations based on this information. The first equation represents the total number of hours worked:

x + y = 54

The second equation represents the total amount earned:

6.55x + 9.20y = 481

Therefore, the correct choice is C.

Question 9

Write a system of equations to describe the problem situation. It is not necessary to solve the problem. Martina has 58 nickels and dimes. She has $3.10 altogether. She has x nickels and y dimes.
A) y = 58 - x, 0.05x + 0.10y = 3.10
B) x + y = 58, 0.05y + 0.10x = 3.10
C) $x + y = 58,0.25 x + 0.10 y = 3.10$
D) x - y = 58, 0.05x + 0.10y = 3.10
E) $x - y = 58,0.05 y + 0.25 x = 3.10$

Accepted Answer

The first equation, y = 58 - x, represents the total number of coins (58) as the sum of nickels (x) and dimes (y). The second equation, 0.05x + 0.10y = 3.10, represents the total value of the coins, with nickels valued at $0.05 each and dimes at $0.10 each.

Question 10

Write a system of equations that will solve the problem. It is not necessary to solve the problem. Ed works on two projects during one month. He works 28 hours longer on one project (y) than on the other (x). He works a total of 186 hours during the month.
A) x + y = 186, x = y + 28
B) x - y = 186, x = y + 28
C) x + y = 186, x = y - 28
D) y - x = 186, y = x - 28
E) x - y = 186, x = y - 28

Accepted Answer

The answer of Write a system of equations that will...

Question 11

Write a system of equations that will solve the problem. It is not necessary to solve the problem. Jacques cuts a 14-decimeter submarine sandwich into two pieces. One piece (y) is 2 decimeters longer than the other (x).
A) x + y = 14, x = y + 2
B) x + y = 14, x = y - 2
C) x - y = 14, x = y + 2
D) y - x = 14, y = x - 2
E) y - x = 14, x = y - 2

Accepted Answer

The first equation x + y = 14 represents the total length of the sandwich. The second equation x = y - 2 represents that one piece is 2 decimeters shorter than the other.

Question 12

Use a table to solve the system of equations. If you use a calculator table, record the TbIStart and $\mathrm { V}_{TbI }$ entered. $$\begin{aligned}
4 x - y & = 14 \
2 x - 3 y & = 12
\end{aligned}$$
A) (4, -1)
B) (2, -2)
C) (3, -2)
D) (3, -3)
E) (4, -2)

Accepted Answer

To solve the system of equations using a table, substitute each choice into both equations to see which one satisfies both. For choice C (3, -2), substituting into the first equation: $4(3) - (-2) = 12 + 2 = 14$, which is true. For the second equation: $2(3) - 3(-2) = 6 + 6 = 12$, which is also true. Thus, (3, -2) is the solution.

Question 13

Write a system of equations that will solve the problem. It is not necessary to solve the problem. Alexandra works for two clients during one month. She works a total of 180 hours during the month. She works 50 hours more for one client (y) than for the other (x).
A) x + y = 180, x = y + 50
B) x - y = 180, x = y + 50
C) y - x = 180, y = x - 50
D) $x + y = 180 , y = x + 50$
E) x + y = 180, x - y = 50

Accepted Answer

The system of equations should include one equation for the total hours worked (x + y = 180) and another equation for the difference in hours worked for each client (y = x + 50, as stated in the problem). The only choice that includes both of these equations is D.

Question 14

Write a system of equations to describe the problem situation. It is not necessary to solve the problem. Nancy has $3.50. She has only dimes (x) and quarters (y). She has 30 coins altogether.
A) x = 30 - y, 0.10x + 0.25y = 3.50
B) $x - y = 30,0.10 x + 0.25 y = 3.50$
C) y - x = 30, 0.10x + 0.25y = 3.50
D) x + y = 30, 0.05x + 0.25y = 3.50
E) $x + y = 30,0.05 y + 0.25 x = 3.50$

Accepted Answer

We can use the system of equations: 
x + y = 30 (since there are 30 coins altogether) 
0.10x + 0.25y = 3.50 (since Nancy has only dimes and quarters and has $3.50 in total) 
Simplifying the first equation, we get x = 30 - y. This can be substituted into the second equation to get 0.10(30-y) + 0.25y = 3.50, which is the same as 3 - 0.15y = 3.50. Solving for y, we get y = 10. Substituting this back into the first equation, we get x = 20. Therefore, Nancy has 20 dimes and 10 quarters. Choice A correctly represents this system of equations.

Question 15

Use a table to solve the system of equations. If you use a calculator table, record the TbIStart and $\mathrm { V}_{TbI }$ entered. $$\begin{array} { l } 
y - 2.8 x = 3.8 \
0.6 x + y = 0.4
\end{array}$$
A) (-1, 2)
B) (0, 1)
C) (-1, 0)
D) (-1, 1)
E) (0, 2)

Accepted Answer

To solve the system of equations using a table, we can first isolate $y$ in both equations to compare their values for different $x$. For the first equation, $y = 2.8x + 3.8$.For the second equation, $y = -0.6x + 0.4$.Setting them equal to each other to find the $x$ value where they intersect:$$2.8x + 3.8 = -0.6x + 0.4$$$$3.4x = -3.4$$$$x = -1$$Substitute $x = -1$ into one of the original equations to find $y$:$$y = 2.8(-1) + 3.8 = -2.8 + 3.8 = 1$$Therefore, the solution to the system of equations is $(-1, 1)$, which corresponds to choice D.

Question 16

Write a system of equations that will solve the problem. It is not necessary to solve the problem. Renee cuts a 12-meter hose into two lengths. One piece (x) is 2 meters longer than the other (y). What is the length of each piece?
A) $x + y = 12 , x = y + 2$
B) $x + y = 12 , y = x + 2$
C) x - y = 12, x = y + 2
D) y - x = 12, y = x - 2
E) x + y = 12, x = y - 2

Accepted Answer

The problem states that one piece (x) is 2 meters longer than the other (y), so we can set up the equation x = y + 2. We also know that the two pieces together make up the original 12-meter hose, so x + y = 12. This gives us a system of equations: x + y = 12 and x = y + 2, which is represented by choice A.

Question 17

Do the graphs of the equations form parallel lines? (It is not necessary to graph them.) $$\begin{array} { l } 
2 x + 2 y = 40 \
y = 30 - x
\end{array}$$
A) yes
B) no
C) insufficient information

Accepted Answer

The equations are in slope-intercept form, y = mx + b. The slope of the first equation is -1 and the slope of the second equation is also -1. Since the slopes are equal, the lines are parallel.

Question 18

Do the graphs of the equations form parallel lines? (It is not necessary to graph them.) $$\begin{array} { l } 
y = 9 - x \
y = 2 + x
\end{array}$$
A) yes
B) no
C) insufficient information

Accepted Answer

The two equations have different slopes (one is -1 and the other is 1), so their graphs cannot be parallel.

Question 19

Write a system of equations to describe the problem situation. It is not necessary to solve the problem. Larry has 26 nickels and quarters. He has $2.20 altogether. He has x nickels and y quarters.
A) x - y = 26, 0.10y + 0.25x = 2.20
B) x + y = 26, 0.10x + 0.25y = 2.20
C) x - y = 26, 0.05x + 0.25y = 2.20
D) x + y = 26, 0.05y + 0.25x = 2.20
E) x = 26 - y, 0.05x + 0.25y = 2.20

Accepted Answer

The answer of Write a system of equations to describe...

Question 20

Use a table to solve the system of equations. If you use a calculator table, record the TbIStart and $\mathrm { V}_{TbI }$ entered. $$\begin{array} { r } 
x - 2 y = 5 \
5 x - 10 y = 3
\end{array}$$
A) (2, 5)
B) (2, 10)
C) (5, 10)
D) (5, 5)
E) no solution

Accepted Answer

The system is inconsistent. The second equation is a multiple of the first, but the constants do not match (5 vs. 3), indicating parallel lines with no intersection point.

Quiz 6: Systems of Equations

Use a table to solve the system of equations. If you use a calculator table, record the TbIStart and $\mathrm { V}_{TbI }$ entered. $\begin{array} { r } x - 2 y = 7 \\2 x + 3 y = 0\end{array}$

Do the graphs of the equations form coincident lines? (It is not necessary to graph them.) $\begin{array} { l } 2 x + y = 4 \\2 y + x = 4\end{array}$

Use a table to solve the system of equations. If you use a calculator table, record the TbIStart and $\mathrm { V}_{TbI }$ entered. $\begin{array} { c } 5 x - 3 y = 11 \\- 20 x + 12 y = - 44\end{array}$

Do the graphs of the equations form parallel lines? (It is not necessary to graph them.) $\begin{array} { l } y = 4 x \\y = \frac { 1 } { 4 } ( 12 + 20 x ) \end{array}$

Do the graphs of the equations form coincident lines? (It is not necessary to graph them.) $\begin{array} { l } y + x = 30 \\2 x = 60 - 2 y\end{array}$

Do the graphs of the equations form coincident lines? (It is not necessary to graph them.) $\begin{array} { l } y = x + 0.04 x \\y = 1.04 x\end{array}$

Do the graphs of the equations form coincident lines? (It is not necessary to graph them.) $\begin{array} { l } y + 100 x = 400 \\y = 100 - 400 x\end{array}$

Write a system of equations to describe the problem situation. It is not necessary to solve the problem. Paolo earns $481 from working 54 total hours at two jobs. He earns $6.55 per hour (x) at the first job and $9.20 per hour (y) at the second job.

Write a system of equations to describe the problem situation. It is not necessary to solve the problem. Martina has 58 nickels and dimes. She has $3.10 altogether. She has x nickels and y dimes.

Write a system of equations that will solve the problem. It is not necessary to solve the problem. Ed works on two projects during one month. He works 28 hours longer on one project (y) than on the other (x) . He works a total of 186 hours during the month.

Write a system of equations that will solve the problem. It is not necessary to solve the problem. Jacques cuts a 14-decimeter submarine sandwich into two pieces. One piece (y) is 2 decimeters longer than the other (x) .

Use a table to solve the system of equations. If you use a calculator table, record the TbIStart and $\mathrm { V}_{TbI }$ entered. $\begin{aligned}4 x - y & = 14 \\2 x - 3 y & = 12\end{aligned}$

Write a system of equations that will solve the problem. It is not necessary to solve the problem. Alexandra works for two clients during one month. She works a total of 180 hours during the month. She works 50 hours more for one client (y) than for the other (x) .

Write a system of equations to describe the problem situation. It is not necessary to solve the problem. Nancy has $3.50. She has only dimes (x) and quarters (y) . She has 30 coins altogether.

Use a table to solve the system of equations. If you use a calculator table, record the TbIStart and $\mathrm { V}_{TbI }$ entered. $\begin{array} { l } y - 2.8 x = 3.8 \\0.6 x + y = 0.4\end{array}$

Write a system of equations that will solve the problem. It is not necessary to solve the problem. Renee cuts a 12-meter hose into two lengths. One piece (x) is 2 meters longer than the other (y) . What is the length of each piece?

Do the graphs of the equations form parallel lines? (It is not necessary to graph them.) $\begin{array} { l } 2 x + 2 y = 40 \\y = 30 - x\end{array}$

Do the graphs of the equations form parallel lines? (It is not necessary to graph them.) $\begin{array} { l } y = 9 - x \\y = 2 + x\end{array}$

Write a system of equations to describe the problem situation. It is not necessary to solve the problem. Larry has 26 nickels and quarters. He has $2.20 altogether. He has x nickels and y quarters.

Use a table to solve the system of equations. If you use a calculator table, record the TbIStart and $\mathrm { V}_{TbI }$ entered. $\begin{array} { r } x - 2 y = 5 \\5 x - 10 y = 3\end{array}$

Quiz 6: Systems of Equations

Use a table to solve the system of equations. If you use a calculator table, record the TbIStart and VTbI\mathrm { V}_{TbI }VTbI​ entered. x−2y=72x+3y=0\begin{array} { r } x - 2 y = 7 \\2 x + 3 y = 0\end{array}x−2y=72x+3y=0​

Do the graphs of the equations form coincident lines? (It is not necessary to graph them.) 2x+y=42y+x=4\begin{array} { l } 2 x + y = 4 \\2 y + x = 4\end{array}2x+y=42y+x=4​

Use a table to solve the system of equations. If you use a calculator table, record the TbIStart and VTbI\mathrm { V}_{TbI }VTbI​ entered. 5x−3y=11−20x+12y=−44\begin{array} { c } 5 x - 3 y = 11 \\- 20 x + 12 y = - 44\end{array}5x−3y=11−20x+12y=−44​

Do the graphs of the equations form parallel lines? (It is not necessary to graph them.) y=4xy=14(12+20x) \begin{array} { l } y = 4 x \\y = \frac { 1 } { 4 } ( 12 + 20 x ) \end{array}y=4xy=41​(12+20x) ​

Do the graphs of the equations form coincident lines? (It is not necessary to graph them.) y+x=302x=60−2y\begin{array} { l } y + x = 30 \\2 x = 60 - 2 y\end{array}y+x=302x=60−2y​

Do the graphs of the equations form coincident lines? (It is not necessary to graph them.) y=x+0.04xy=1.04x\begin{array} { l } y = x + 0.04 x \\y = 1.04 x\end{array}y=x+0.04xy=1.04x​

Do the graphs of the equations form coincident lines? (It is not necessary to graph them.) y+100x=400y=100−400x\begin{array} { l } y + 100 x = 400 \\y = 100 - 400 x\end{array}y+100x=400y=100−400x​