Question 1

Use the given row transformation to change the matrix as indicated.
-$\left[ \begin{array} { c c } - 2 & 3 \ 14 & 0 \end{array} \right] ; 7$ times row 1 added to row 2
A)
$\left[ \begin{array} { r r } - 14 & 21 \ 14 & 0 \end{array} \right]$

B)
$\left[\begin{array}{rr}
-2 & 3 \
0 & 21
\end{array}\right]$

C)
$\left[\begin{array}{rr}
-2 & -11 \
0 & 21
\end{array}\right]$

D)
$\left[\begin{array}{rr}
-2 & 3 \
14 & 21
\end{array}\right]$

Accepted Answer

To perform the row operation, multiply row 1 by 7 and add it to row 2. For row 1, $(-2) \times 7 = -14$ and $3 \times 7 = 21$. Adding these to row 2 gives $14 + (-14) = 0$ and $0 + 21 = 21$, resulting in the matrix in option B.

Question 2

Write the augmented matrix for the system. Do not solve the system.
-$$\begin{array} { l } 
9 x + 3 y = 78 \
7 x + 5 y = 58
\end{array}$$
A)
$\left[\begin{array}{ll|l}
9 & 7 & 78 \
3 & 5 & 58
\end{array}\right]$

B)
$\left[\begin{array}{ll|l}
78 & 3 & 9 \
58 & 7 & 5
\end{array}\right]$

C)
$\left[\begin{array}{ll|l}
9 & 3 & 58 \
5 & 7 & 78
\end{array}\right]$

D)
$\left[\begin{array}{ll|l}
9 & 3 & 78 \
7 & 5 & 58
\end{array}\right]$

Accepted Answer

The augmented matrix is formed by writing the coefficients of the variables in the system of equations in the same order as they appear, followed by the constants on the right side of the equality, separated by a line. Option D correctly represents the system of equations given.

Question 3

Provide an appropriate response.
-If the graphs of a system of two equations are both parabolas, what are the possible
numbers of solutions (with real coordinates) of this system?

Accepted Answer

The answer of Provide an appropriate response.
-If the graphs of...

Question 4

Write the augmented matrix for the system. Do not solve the system.
-$$\begin{array} { r } 
9 x + 7 y = 93 \
2 y = 6
\end{array}$$
A)
$\left[\begin{array}{rr|r}
93 & 7 & 9 \
6 & 0 & 2
\end{array}\right]$

B)
$\left[\begin{array}{rr|r}
9 & 7 & 93 \
2 & 6 & 0
\end{array}\right]$

C)
$\left[\begin{array}{ll|l}
2 & 0 & 6 \
9 & 7 & 7
\end{array}\right]$
D)
$\left[\begin{array}{rr|r}
9 & 7 & 93 \
0 & 2 & 6
\end{array}\right]$

Accepted Answer

The augmented matrix correctly represents the system of equations with coefficients of $x$ and $y$ in the first two columns and the constants on the right side of the bar. The first row corresponds to $9x + 7y = 93$, and the second row to $0x + 2y = 6$, correctly placing the coefficients and constants in their respective positions.

Question 5

Write the augmented matrix for the system. Do not solve the system.
-$$\begin{array} { l } 
5 x + 5 y = 15 \
7 x + 9 y = 17
\end{array}$$
A)
$\left[ \begin{array} { l l | l } 5 & 7 & 15 \ 5 & 9 & 17 \end{array} \right]$
B)
$\left[ \begin{array} { l l | l } 5 & 5 & 17 \ 9 & 7 & 15 \end{array} \right]$
C)
$\left[ \begin{array} { l l | l } 15 & 5 & 5 \ 17 & 7 & 9 \end{array} \right]$

D)
$\left[ \begin{array} { l l | l } 5 & 5 & 15 \ 7 & 9 & 17 \end{array} \right]$

Accepted Answer

The augmented matrix for the given system of equations is formed by writing the coefficients of $x$ and $y$ in the first two columns, and the constants on the right side of the equation in the third column, maintaining the order of equations and their respective terms.

Question 6

Provide an appropriate response.
-If the graphs of a system of two equations are a line and a parabola, what are the possible
numbers of solutions (with real coordinates) of this system?

Accepted Answer

The answer of Provide an appropriate response.
-If the graphs of...

Question 7

Provide an appropriate response.
-2x - 7y = -17
5x + 3y = 19
If your friend were going to solve this system of equations by first eliminating y, what
general suggestions would you make so your friend could start on this in a systematic
way?

Accepted Answer

The answer of Provide an appropriate response.
-2x - 7y =...

Question 8

Provide an appropriate response.
-If the graphs of a system of two equations are a circle and a parabola, what are the
possible numbers of solutions (with real coordinates) of this system?

Accepted Answer

The answer of Provide an appropriate response.
-If the graphs of...

Question 9

Use the given row transformation to change the matrix as indicated.
-$\left[ \begin{array} { r r r } 3 & 5 & 12 \ 1 & 3 & 2 \ 2 & - 3 & 3 \end{array} \right] ; - 2$ times row 2 added to row 3
A)
$\left[ \begin{array} { r r r } 3 & 5 & 12 \ 1 & 3 & 2 \ 0 & - 6 & 1 \end{array} \right]$

B)
$\left[ \begin{array} { r r r } 3 & 5 & 12 \ 1 & 3 & 2 \ 0 & - 9 & - 1 \end{array} \right]$
C)
$\left[\begin{array}{rrr}
3 & 5 & 12 \
1 & 3 & 2 \
4 & 3 & 7
\end{array}\right]$

D)
$$\left[ \begin{array} { r r r } 
1 & - 1 & 8 \
1 & 3 & 2 \
2 & - 3 & 3
\end{array} \right]$$

Accepted Answer

To perform the row operation "-2 times row 2 added to row 3", we multiply each element in row 2 by -2 and add the result to the corresponding element in row 3. For row 2, the elements are (1, 3, 2). Multiplying by -2 gives (-2, -6, -4). Adding these to row 3's elements (2, -3, 3) gives (0, -9, -1), which matches option B.

Question 10

Provide an appropriate response.
-5x + 3y = 19
7x + 8y = 48
If your friend were going to solve this system of equations by first eliminating y, what
general suggestions would you make so your friend could start on this in a systematic
way?

Accepted Answer

The answer of Provide an appropriate response.
-5x + 3y =...

Question 11

Provide an appropriate response.
-When using the substitution or elimination method to solve a system of two equations,
you end up with an equation stating 0 = 0. What does this indicate to you about the
system of equations?

Accepted Answer

The answer of Provide an appropriate response.
-When using the substitution...

Question 12

Provide an appropriate response.
-When using the substitution or elimination method to solve a system of two equations,
you end up with an equation stating 0 = 7. What does this indicate to you about the
system of equations?

Accepted Answer

The answer of Provide an appropriate response.
-When using the substitution...

Question 13

Write the augmented matrix for the system. Do not solve the system.
-$$\begin{aligned}
7 x - 2 z & = - 9 \
2 y + 7 z & = 9 \
7 x + 9 y + 4 z & = 6
\end{aligned}$$
A)
$\left[ \begin{array} { r r r } 7 & 0 & - 2 \ 0 & 2 & 7 \ 7 & 9 & 4 \end{array} \right]$

B)
$\left[ \begin{array} { r r r | r } 7 & 0 & 7 & - 9 \ 0 & 2 & 9 & 9 \ - 2 & 7 & 4 & 6 \end{array} \right]$

C)
$\left[ \begin{array} { r r r | r } 7 & 0 & - 2 & - 9 \ 0 & 2 & 7 & 9 \ 7 & 9 & 4 & 6 \end{array} \right]$

D)

$\left[ \begin{array} { r r r | r } 7 & - 2 & 0 & - 9 \ 2 & 7 & 0 & 9 \ 7 & 9 & 4 & 6 \end{array} \right]$

Accepted Answer

The augmented matrix correctly represents the system of equations with the coefficients of $x$, $y$, and $z$ in the first three columns and the constants on the right side of the equation in the fourth column.

Question 14

Use the given row transformation to change the matrix as indicated.
-$\left[\begin{array}{rrr}
6 & 5 & 6 \
5 & -2 & 7 \
5 & 3 & 1
\end{array}\right] ;-6 \text { times row } 3 \text { added to row } 1$
A)
$\left[\begin{array}{rrr}
6 & 5 & 1 \
5 & -2 & 7 \
-30 & -18 & -6
\end{array}\right]$

B)
$\left[\begin{array}{ccr}
6 & 5 & 6 \
-25 & -20 & 1 \
-30 & -18 & -6
\end{array}\right]$

C)
$\left[\begin{array}{rrr}
11 & 8 & 0 \
5 & -2 & 7 \
5 & 3 & 1
\end{array}\right]$

D)
$\left[\begin{array}{ccc}
-24 & -13 & 0 \
5 & -2 & 7 \
5 & 3 & 1
\end{array}\right]$

Accepted Answer

To apply the transformation, multiply each element of row 3 by -6 and add it to the corresponding element of row 1: $6 + (-6 \times 5) = -24$, $5 + (-6 \times 3) = -13$, $6 + (-6 \times 1) = 0$.

Question 15

Use the given row transformation to change the matrix as indicated.
-$\left[ \begin{array} { l l } 2 & 3 \ 4 & 7 \end{array} \right] ; - 2$ times row 1 added to row 2
A)
$\left[ \begin{array} { l l } 2 & 3 \ 1 & 1 \end{array} \right]$
B)
$\left[ \begin{array} { l l } 2 & 3 \ 0 & 1 \end{array} \right]$
C)
$\left[ \begin{array} { r r } - 4 & - 6 \ 0 & 1 \end{array} \right]$
D)
$\left[ \begin{array} { r r } 2 & 3 \ 0 & - 1 \end{array} \right]$

Accepted Answer

The answer of Use the given row transformation to change...

Question 16

Provide an appropriate response.
-If the graphs of a system of two equations are both circles, what are the possible numbers
of solutions (with real coordinates) of this system?

Accepted Answer

The answer of Provide an appropriate response.
-If the graphs of...

Question 17

The solution set of the system $y _ { 1 } = 2 x + 3$ and $y _ { 2 } = - x + 9$ is $\{ ( 2,7 ) \}$. Using slopes and $y$-intercepts, determine which of the two calculator-generated screens, left or right, is the appropriate one for this system.

A) Left
B) Right
C) Neither is correct.
D) Both could be correct.

Accepted Answer

The answer of The solution set of the system \(y...

Question 18

Use the given row transformation to change the matrix as indicated.
-$\left[ \begin{array} { r r r } 2 & 1 & 4 \ - 4 & 3 & - 1 \ 7 & 4 & 0 \end{array} \right] ; 2$ times row 1 added to row 2
A)
$\left[ \begin{array} { l l l } 2 & 1 & 4 \ 0 & 5 & 7 \ 7 & 4 & 0 \end{array} \right]$

B)
$\left[ \begin{array} { r r r } 2 & 1 & 4 \ - 4 & 3 & - 1 \ 11 & 6 & 8 \end{array} \right]$

C)
$\left[\begin{array}{lll}
2 & 1 & 4 \
0 & 3 & 7 \
7 & 4 & 0
\end{array}\right]$
D)
$\left[\begin{array}{lll}
4 & 2 & 8 \
0 & 5 & 7 \
7 & 4 & 0
\end{array}\right]$

Accepted Answer

Multiplying row 1 by 2 gives [4, 2, 8]. Adding this to row 2, which is [-4, 3, -1], results in [0, 5, 7] for the new row 2, matching option A.

Question 19

Write the augmented matrix for the system. Do not solve the system.
-$$\begin{array} { l } 
3 x + 6 y - 2 z = 41 \
6 x + 5 y + 3 z = 26 \
2 x + 8 y + 7 z = 47
\end{array}$$
A)
$$\left[ \begin{array} { r r r | r } 
3 & 6 & 2 & 41 \
6 & 5 & 8 & 26 \
- 2 & 3 & 7 & 47
\end{array} \right]$$
B)
$\left[ \begin{array} { r r r | r } 3 & 6 & - 2 & 41 \ 6 & 5 & 3 & 26 \ 2 & 8 & 7 & 47 \end{array} \right]$
C)
$\left[ \begin{array} { r r r | r } 41 & - 2 & 6 & 3 \ 26 & 3 & 5 & 6 \ 47 & 7 & 8 & 2 \end{array} \right]$
D)
$\left[ \begin{array} { r r r } 3 & 6 & - 2 \ 6 & 5 & 3 \ 2 & 8 & 7 \end{array} \right]$

Accepted Answer

The augmented matrix for the given system of equations correctly aligns the coefficients of $x$, $y$, and $z$ in the first three columns and the constants on the right side of the equation in the fourth column, as shown in choice B.

Question 20

The solution set of the system $y _ { 1 } = - x + 5$ and $y _ { 2 } = - 2 x + 7$ is $\{ ( 2,3 ) \}$. Using slopes and $y$-intercepts, determine which of the two calculator-generated screens, left or right, is the appropriate one for this system.

A) Left
B) Right
C) Neither is correct.
D) Both could be correct.

Accepted Answer

The answer of The solution set of the system \(y...

Quiz 9: Systems and Matrices

Use the given row transformation to change the matrix as indicated. - $\left[ \begin{array} { c c } - 2 & 3 \\ 14 & 0 \end{array} \right] ; 7$ times row 1 added to row 2

Write the augmented matrix for the system. Do not solve the system. - $\begin{array} { l } 9 x + 3 y = 78 \\7 x + 5 y = 58\end{array}$

Provide an appropriate response. -If the graphs of a system of two equations are both parabolas, what are the possible numbers of solutions (with real coordinates) of this system?

Write the augmented matrix for the system. Do not solve the system. - $\begin{array} { r } 9 x + 7 y = 93 \\2 y = 6\end{array}$

Write the augmented matrix for the system. Do not solve the system. - $\begin{array} { l } 5 x + 5 y = 15 \\7 x + 9 y = 17\end{array}$

Provide an appropriate response. -If the graphs of a system of two equations are a line and a parabola, what are the possible numbers of solutions (with real coordinates) of this system?

Provide an appropriate response. -2x - 7y = -17 5x + 3y = 19 If your friend were going to solve this system of equations by first eliminating y, what general suggestions would you make so your friend could start on this in a systematic way?

Provide an appropriate response. -If the graphs of a system of two equations are a circle and a parabola, what are the possible numbers of solutions (with real coordinates) of this system?

Use the given row transformation to change the matrix as indicated. - $\left[ \begin{array} { r r r } 3 & 5 & 12 \\ 1 & 3 & 2 \\ 2 & - 3 & 3 \end{array} \right] ; - 2$ times row 2 added to row 3

Provide an appropriate response. -5x + 3y = 19 7x + 8y = 48 If your friend were going to solve this system of equations by first eliminating y, what general suggestions would you make so your friend could start on this in a systematic way?

Provide an appropriate response. -When using the substitution or elimination method to solve a system of two equations, you end up with an equation stating 0 = 0. What does this indicate to you about the system of equations?

Provide an appropriate response. -When using the substitution or elimination method to solve a system of two equations, you end up with an equation stating 0 = 7. What does this indicate to you about the system of equations?

Write the augmented matrix for the system. Do not solve the system. - $\begin{aligned}7 x - 2 z & = - 9 \\2 y + 7 z & = 9 \\7 x + 9 y + 4 z & = 6\end{aligned}$

Use the given row transformation to change the matrix as indicated. - $\left[\begin{array}{rrr}6 & 5 & 6 \\5 & -2 & 7 \\5 & 3 & 1\end{array}\right] ;-6 \text { times row } 3 \text { added to row } 1$

Use the given row transformation to change the matrix as indicated. - $\left[ \begin{array} { l l } 2 & 3 \\ 4 & 7 \end{array} \right] ; - 2$ times row 1 added to row 2

Provide an appropriate response. -If the graphs of a system of two equations are both circles, what are the possible numbers of solutions (with real coordinates) of this system?

Use the given row transformation to change the matrix as indicated. - $\left[ \begin{array} { r r r } 2 & 1 & 4 \\ - 4 & 3 & - 1 \\ 7 & 4 & 0 \end{array} \right] ; 2$ times row 1 added to row 2

Write the augmented matrix for the system. Do not solve the system. - $\begin{array} { l } 3 x + 6 y - 2 z = 41 \\6 x + 5 y + 3 z = 26 \\2 x + 8 y + 7 z = 47\end{array}$

Quiz 9: Systems and Matrices

Use the given row transformation to change the matrix as indicated. - [−23140];7\left[ \begin{array} { c c } - 2 & 3 \\ 14 & 0 \end{array} \right] ; 7[−214​30​];7 times row 1 added to row 2

Write the augmented matrix for the system. Do not solve the system. - 9x+3y=787x+5y=58\begin{array} { l } 9 x + 3 y = 78 \\7 x + 5 y = 58\end{array}9x+3y=787x+5y=58​

Provide an appropriate response. -If the graphs of a system of two equations are both parabolas, what are the possible numbers of solutions (with real coordinates) of this system?

Write the augmented matrix for the system. Do not solve the system. - 9x+7y=932y=6\begin{array} { r } 9 x + 7 y = 93 \\2 y = 6\end{array}9x+7y=932y=6​

Write the augmented matrix for the system. Do not solve the system. - 5x+5y=157x+9y=17\begin{array} { l } 5 x + 5 y = 15 \\7 x + 9 y = 17\end{array}5x+5y=157x+9y=17​

Provide an appropriate response. -If the graphs of a system of two equations are a line and a parabola, what are the possible numbers of solutions (with real coordinates) of this system?

Provide an appropriate response. -2x - 7y = -17 5x + 3y = 19 If your friend were going to solve this system of equations by first eliminating y, what general suggestions would you make so your friend could start on this in a systematic way?

Provide an appropriate response. -If the graphs of a system of two equations are a circle and a parabola, what are the possible numbers of solutions (with real coordinates) of this system?

Use the given row transformation to change the matrix as indicated. - [35121322−33];−2\left[ \begin{array} { r r r } 3 & 5 & 12 \\ 1 & 3 & 2 \\ 2 & - 3 & 3 \end{array} \right] ; - 2​312​53−3​1223​​;−2 times row 2 added to row 3

Provide an appropriate response. -5x + 3y = 19 7x + 8y = 48 If your friend were going to solve this system of equations by first eliminating y, what general suggestions would you make so your friend could start on this in a systematic way?

Provide an appropriate response. -When using the substitution or elimination method to solve a system of two equations, you end up with an equation stating 0 = 0. What does this indicate to you about the system of equations?

Provide an appropriate response. -When using the substitution or elimination method to solve a system of two equations, you end up with an equation stating 0 = 7. What does this indicate to you about the system of equations?

Write the augmented matrix for the system. Do not solve the system. - 7x−2z=−92y+7z=97x+9y+4z=6\begin{aligned}7 x - 2 z & = - 9 \\2 y + 7 z & = 9 \\7 x + 9 y + 4 z & = 6\end{aligned}7x−2z2y+7z7x+9y+4z​=−9=9=6​

Use the given row transformation to change the matrix as indicated. - [2347];−2\left[ \begin{array} { l l } 2 & 3 \\ 4 & 7 \end{array} \right] ; - 2[24​37​];−2 times row 1 added to row 2

Provide an appropriate response. -If the graphs of a system of two equations are both circles, what are the possible numbers of solutions (with real coordinates) of this system?

The solution set of the system y1=2x+3y _ { 1 } = 2 x + 3y1​=2x+3 and y2=−x+9y _ { 2 } = - x + 9y2​=−x+9 is {(2,7) }\{ ( 2,7 ) \}{(2,7) } . Using slopes and yyy -intercepts, determine which of the two calculator-generated screens, left or right, is the appropriate one for this system.

Use the given row transformation to change the matrix as indicated. - [214−43−1740];2\left[ \begin{array} { r r r } 2 & 1 & 4 \\ - 4 & 3 & - 1 \\ 7 & 4 & 0 \end{array} \right] ; 2​2−47​134​4−10​​;2 times row 1 added to row 2

Write the augmented matrix for the system. Do not solve the system. - 3x+6y−2z=416x+5y+3z=262x+8y+7z=47\begin{array} { l } 3 x + 6 y - 2 z = 41 \\6 x + 5 y + 3 z = 26 \\2 x + 8 y + 7 z = 47\end{array}3x+6y−2z=416x+5y+3z=262x+8y+7z=47​

Use the given row transformation to change the matrix as indicated. - $\left[ \begin{array} { c c } - 2 & 3 \\ 14 & 0 \end{array} \right] ; 7$ times row 1 added to row 2

Write the augmented matrix for the system. Do not solve the system. - $\begin{array} { l } 9 x + 3 y = 78 \\7 x + 5 y = 58\end{array}$

Write the augmented matrix for the system. Do not solve the system. - $\begin{array} { r } 9 x + 7 y = 93 \\2 y = 6\end{array}$

Write the augmented matrix for the system. Do not solve the system. - $\begin{array} { l } 5 x + 5 y = 15 \\7 x + 9 y = 17\end{array}$

Use the given row transformation to change the matrix as indicated. - $\left[ \begin{array} { r r r } 3 & 5 & 12 \\ 1 & 3 & 2 \\ 2 & - 3 & 3 \end{array} \right] ; - 2$ times row 2 added to row 3

Write the augmented matrix for the system. Do not solve the system. - $\begin{aligned}7 x - 2 z & = - 9 \\2 y + 7 z & = 9 \\7 x + 9 y + 4 z & = 6\end{aligned}$

Use the given row transformation to change the matrix as indicated. - $\left[ \begin{array} { l l } 2 & 3 \\ 4 & 7 \end{array} \right] ; - 2$ times row 1 added to row 2

Use the given row transformation to change the matrix as indicated. - $\left[ \begin{array} { r r r } 2 & 1 & 4 \\ - 4 & 3 & - 1 \\ 7 & 4 & 0 \end{array} \right] ; 2$ times row 1 added to row 2

Write the augmented matrix for the system. Do not solve the system. - $\begin{array} { l } 3 x + 6 y - 2 z = 41 \\6 x + 5 y + 3 z = 26 \\2 x + 8 y + 7 z = 47\end{array}$