Question 1

Use the graphs in the illustration to solve the equation. $- x - 4 = 2 x - 1$

Accepted Answer

A)  x=1 
B)  x=-1 
C)  x=2 
D)  x=-2 
E)  x=3 
A)  x=1 
B)  x=-1 
C)  x=2 
D)  x=-2 
E)  x=3

Question 2

Refer to the illustration. Answer the questions.  
 How many solutions does the system of equations have? Are the equations dependent or independent?

Accepted Answer

A)  no solution, independent equations 
B)  no solution, dependent equations 
C)  infinite number of solutions, dependent equations 
D)  two solutions, independent equations 
E)  one solution, independent equations 
A)  no solution, independent equations 
B)  no solution, dependent equations 
C)  infinite number of solutions, dependent equations 
D)  two solutions, independent equations 
E)  one solution, independent equations

Question 3

Which matrix indicates that the equations of its associated system of equations has infinitely many solutions?

Accepted Answer

A)  $\left[ \begin{array} { c c : c } 
1 & - 9 & 5 \
0 & 1 & 1
\end{array} \right]$ 
B)  $\left[ \begin{array} { c c : c } 
1 & - 9 & 5 \
0 & 0 & 6
\end{array} \right]$ 
C)  $\left[ \begin{array} { c c : c } 
1 & - 2 & 3 \
0 & 0 & 0
\end{array} \right]$ 
D)  $\left[ \begin{array} { l l : l } 
1 & 0 & 5 \
0 & 1 & 1
\end{array} \right]$ 
A)  $\left[ \begin{array} { c c : c } 
1 & - 9 & 5 \
0 & 1 & 1
\end{array} \right]$ 
B)  $\left[ \begin{array} { c c : c } 
1 & - 9 & 5 \
0 & 0 & 6
\end{array} \right]$ 
C)  $\left[ \begin{array} { c c : c } 
1 & - 2 & 3 \
0 & 0 & 0
\end{array} \right]$ 
D)  $\left[ \begin{array} { l l : l } 
1 & 0 & 5 \
0 & 1 & 1
\end{array} \right]$

Question 4

Evaluate the determinant $\left| \begin{array} { l l } 
9 & - 3 \
0 & - 4
\end{array} \right|$

Accepted Answer

A)  36 
B)  -96 
C)  96 
D)  -36 
A)  36 
B)  -96 
C)  96 
D)  -36

Question 5

A total of $25,000 was invested in two accounts for one year and the amount earned was $1,550. Part of the money was invested at 6% and the rest at 7%. Write a system of two equations in two unknowns that would model the situation. Let x = amount invested at 6% and y = amount invested at 7%.

Accepted Answer

A)  $\left\{ \begin{array} { l } 
x + y = 1,550 \
.06 x + .07 y = 25,000
\end{array} \right.$ 
B)  $\left\{ \begin{array} { l } 
x + y = 25,000 \
.6 x + 7 y = 1,550
\end{array} \right.$ 
C)  $\left\{ \begin{array} { l } 
x + y = 1,550 \
.6 x + 7 y = 25,000
\end{array} \right.$ 
D)  $\left\{ \begin{array} { l } 
x + y = 25,000 \
.06 x + .07 y = 1,550
\end{array} \right.$ 
A)  $\left\{ \begin{array} { l } 
x + y = 1,550 \
.06 x + .07 y = 25,000
\end{array} \right.$ 
B)  $\left\{ \begin{array} { l } 
x + y = 25,000 \
.6 x + 7 y = 1,550
\end{array} \right.$ 
C)  $\left\{ \begin{array} { l } 
x + y = 1,550 \
.6 x + 7 y = 25,000
\end{array} \right.$ 
D)  $\left\{ \begin{array} { l } 
x + y = 25,000 \
.06 x + .07 y = 1,550
\end{array} \right.$

Question 6

Find the x -coordinate of the solution of the following system. Use the method of elimination. $( - 5 + 3 i ) - ( 3 - i )$

Accepted Answer

A)  $- 8 + 2 i$ 
B)  $2 + 2 i$ 
C)  $- 2 + 4 i$ 
D)  $- 8 + 4 i$ 
A)  $- 8 + 2 i$ 
B)  $2 + 2 i$ 
C)  $- 2 + 4 i$ 
D)  $- 8 + 4 i$

Question 7

Solve the system. Give your answer as an ordered triple in the form of ( a, b, c ). 
$\left\{ \begin{array} { l } 
2 a + 3 b - 2 c = 18 \
5 a - 6 b + c = 15 \
4 b - 2 c - 6 = 0
\end{array} \right.$

Accepted Answer

A)  $( 12,8,13 )$ 
B)  $( 10,9,13 )$ 
C)  $( 10,8,13 )$ 
D)  The system is inconsistent. 
E)  The equations are dependent. 
A)  $( 12,8,13 )$ 
B)  $( 10,9,13 )$ 
C)  $( 10,8,13 )$ 
D)  The system is inconsistent. 
E)  The equations are dependent.

Question 8

Use the method of substitution to find the x -coordinate of the solution of the following system of equations. $a + b i$

Accepted Answer

A)  $( 5 - 2 i ) ( 2 + 5 i )$ 
B)  $12 + 5 i$ 
C)  $16 + 21 i$ 
D)  $14 - 2 i$ 
A)  $( 5 - 2 i ) ( 2 + 5 i )$ 
B)  $12 + 5 i$ 
C)  $16 + 21 i$ 
D)  $14 - 2 i$

Question 9

An artist makes three types of ceramic statues at a monthly cost of $650 for 165 statues. The manufacturing costs for the three types are $5, $4, and $3. If the statues sell for $20, $12, and $9, respectively, how many of each type should be made to produce $2,100 in monthly revenue?

Accepted Answer

A)  23 expensive, 96 middle-priced, 46 inexpensive 
B)  25 expensive, 97 middle-priced, 43 inexpensive 
C)  31 expensive, 91 middle-priced, 43 inexpensive 
D)  30 expensive, 95 middle-priced, 40 inexpensive 
E)  28 expensive, 98 middle-priced, 39 inexpensive 
A)  23 expensive, 96 middle-priced, 46 inexpensive 
B)  25 expensive, 97 middle-priced, 43 inexpensive 
C)  31 expensive, 91 middle-priced, 43 inexpensive 
D)  30 expensive, 95 middle-priced, 40 inexpensive 
E)  28 expensive, 98 middle-priced, 39 inexpensive

Question 10

Determine whether the ordered pair $\left( \frac { 1 } { 3 } , \frac { 1 } { 2 } \right)$ is a solution of the following system. $\left\{ \begin{array} { c } 
6 x - 8 y = - 2 \
- 6 x + 10 y = 3
\end{array} \right.$

Accepted Answer

A)  not a solution 
B)  solution 
A)  not a solution 
B)  solution

Question 11

Find the equation of the form $y = a x ^ { 2 } + b x + c$ for the parabola shown in the illustration.

Accepted Answer

A)  $y = - x ^ { 2 } + 2 x - 4$ 
B)  $y = - x ^ { 2 } - 2 x + 4$ 
C)  $y = x ^ { 2 } - 2 x - 4$ 
D)  $y = x ^ { 2 } + 2 x + 6$ 
E)  $y = x ^ { 2 } + 2 x - 6$ 
A)  $y = - x ^ { 2 } + 2 x - 4$ 
B)  $y = - x ^ { 2 } - 2 x + 4$ 
C)  $y = x ^ { 2 } - 2 x - 4$ 
D)  $y = x ^ { 2 } + 2 x + 6$ 
E)  $y = x ^ { 2 } + 2 x - 6$

Question 12

Find the augmented matrix that represents the system of $\left\{ \begin{array} { l } 
7 x - 9 y = 3 \
7 x - 4 = 7 y
\end{array} \right.$ .

Accepted Answer

A)  $\left[ \begin{array} { l l : l } 
7 & - 9 & 3 \
7 & - 4 & 7
\end{array} \right]$ 
B)  $\left[ \begin{array} { c c : c } 
7 & 9 & 3 \
7 & - 4 & 7
\end{array} \right]$ 
C)  $\left[ \begin{array} { c c : c } 
7 & - 9 & 3 \
7 & - 7 & - 4
\end{array} \right]$ 
D)  $\left[ \begin{array} { l l : l } 
7 & - 9 & 3 \
7 & - 7 & 4
\end{array} \right]$ 
A)  $\left[ \begin{array} { l l : l } 
7 & - 9 & 3 \
7 & - 4 & 7
\end{array} \right]$ 
B)  $\left[ \begin{array} { c c : c } 
7 & 9 & 3 \
7 & - 4 & 7
\end{array} \right]$ 
C)  $\left[ \begin{array} { c c : c } 
7 & - 9 & 3 \
7 & - 7 & - 4
\end{array} \right]$ 
D)  $\left[ \begin{array} { l l : l } 
7 & - 9 & 3 \
7 & - 7 & 4
\end{array} \right]$

Question 13

How many pounds of peanuts selling for $5 per pound should be mixed with cashews selling for $8 per pound to obtain 40 pounds of mixed nuts selling for $7 per pound? Write a system of two equations in two unknowns that would model the situation. Let x = number of pounds of peanuts and y = number of pounds of cashews.

Accepted Answer

A)  $\left\{ \begin{array} { l } 
x + y = 40 \
5 x + 8 y = 40
\end{array} \right.$ 
B)  $\left\{ \begin{array} { l } 
x + y = 40 \
5 x + 8 y = 280
\end{array} \right.$ 
C)  $\left\{ \begin{array} { l } 
x + y = 280 \
5 x + 8 y = 40
\end{array} \right.$ 
D)  $\left\{ \begin{array} { l } 
x + 40 = y \
5 x + 8 y = 280
\end{array} \right.$ 
A)  $\left\{ \begin{array} { l } 
x + y = 40 \
5 x + 8 y = 40
\end{array} \right.$ 
B)  $\left\{ \begin{array} { l } 
x + y = 40 \
5 x + 8 y = 280
\end{array} \right.$ 
C)  $\left\{ \begin{array} { l } 
x + y = 280 \
5 x + 8 y = 40
\end{array} \right.$ 
D)  $\left\{ \begin{array} { l } 
x + 40 = y \
5 x + 8 y = 280
\end{array} \right.$

Question 14

Use Cramer s Rule to solve the system for z. $\left\{ \begin{array} { l } 
x + y - z = 4 \
8 x - 6 y + 7 z = 1 \
x + 9 y - z = - 2
\end{array} \right.$

Accepted Answer

A)  $z = \frac { \left| \begin{array} { c c c } 
4 & 1 & - 1 \
1 & - 6 & 7 \
- 2 & 9 & - 1
\end{array} \right| } { \left| \begin{array} { c c c } 
1 & 1 & - 1 \
8 & - 6 & 7 \
1 & 9 & - 1
\end{array} \right| }$ 
B)  $z = \frac { \left| \begin{array} { c c c } 
1 & 1 & 4 \
8 & - 6 & 1 \
1 & 9 & - 2
\end{array} \right| } { \left| \begin{array} { c c c } 
1 & 1 & - 1 \
8 & - 6 & 7 \
1 & 9 & - 1
\end{array} \right| }$ 
C)  $z = \frac { \left| \begin{array} { c c c } 
1 & 4 & - 1 \
8 & 1 & 7 \
1 & 9 & - 2
\end{array} \right| } { \left| \begin{array} { c c c } 
1 & 1 & - 1 \
8 & - 6 & 7 \
1 & 9 & - 1
\end{array} \right| }$ 
D)  $z = \frac { \left| \begin{array} { c c c } 
1 & 1 & - 1 \
8 & - 6 & 7 \
1 & 9 & - 1
\end{array} \right| } { \left| \begin{array} { c c c } 
1 & 1 & 4 \
8 & - 6 & 1 \
1 & 9 & - 2
\end{array} \right| }$ 
A)  $z = \frac { \left| \begin{array} { c c c } 
4 & 1 & - 1 \
1 & - 6 & 7 \
- 2 & 9 & - 1
\end{array} \right| } { \left| \begin{array} { c c c } 
1 & 1 & - 1 \
8 & - 6 & 7 \
1 & 9 & - 1
\end{array} \right| }$ 
B)  $z = \frac { \left| \begin{array} { c c c } 
1 & 1 & 4 \
8 & - 6 & 1 \
1 & 9 & - 2
\end{array} \right| } { \left| \begin{array} { c c c } 
1 & 1 & - 1 \
8 & - 6 & 7 \
1 & 9 & - 1
\end{array} \right| }$ 
C)  $z = \frac { \left| \begin{array} { c c c } 
1 & 4 & - 1 \
8 & 1 & 7 \
1 & 9 & - 2
\end{array} \right| } { \left| \begin{array} { c c c } 
1 & 1 & - 1 \
8 & - 6 & 7 \
1 & 9 & - 1
\end{array} \right| }$ 
D)  $z = \frac { \left| \begin{array} { c c c } 
1 & 1 & - 1 \
8 & - 6 & 7 \
1 & 9 & - 1
\end{array} \right| } { \left| \begin{array} { c c c } 
1 & 1 & 4 \
8 & - 6 & 1 \
1 & 9 & - 2
\end{array} \right| }$

Question 15

Solve the system by substitution, if possible. If the equations of the system are dependent, or if the system is inconsistent, so indicate. $i$

Accepted Answer

The answer of Solve the system by substitution, if possible....

Question 16

The graph of the equation $5 x + 8 y + 7 z = 6$ is a flat surface called a __________.

Accepted Answer

A)  intersection 
B)  cylinder 
C)  plane 
D)  curve 
E)  triple 
A)  intersection 
B)  cylinder 
C)  plane 
D)  curve 
E)  triple

Question 17

When we add the two equations of the system $\log _ { 5 } ( 2 x - 7 ) = \log _ { 5 } ( x + 1 )$ , the y -terms are __________.

Accepted Answer

The answer of When we add the two equations of...

Question 18

Solve the system $\left\{ \begin{array} { l } 
x - 6 y = 9 \
4 x - 5 y = 17
\end{array} \right.$ by matrices.

Accepted Answer

A)  (6,-1) 
B)  (3,-1) 
C)  $\left( - \frac { 4 } { 7 } , 1 \right)$ 
D)  (3,1) 
A)  (6,-1) 
B)  (3,-1) 
C)  $\left( - \frac { 4 } { 7 } , 1 \right)$ 
D)  (3,1)

Question 19

The owner of a home decorating shop wants to mix dried rose petals selling for $7 per pound, dried lavender selling for $4 per pound, and buckwheat hulls selling for $2 per pound to get 20 pounds of a mixture that would sell for $4.40 per pound. She wants to use twice as many pounds of rose petals as lavender. How many pounds of each should she use?
 __________ lb of rose petals, __________ lb of lavender, __________ lb of buckwheat hulls

Accepted Answer

The answer of The owner of a home decorating shop...

Question 20

Which matrix shown below indicates that the equations of its associated system are dependent?

Accepted Answer

A)  $\left[ \begin{array} { c c | c } 
1 & 6 & - 7 \
0 & 3 & 0
\end{array} \right]$ 
B)  $\left[ \begin{array} { c c | c } 
1 & 6 & - 7 \
0 & 0 & 5
\end{array} \right]$ 
C)  $\left[ \begin{array} { c c | c } 
1 & 6 & - 7 \
0 & 8 & 0
\end{array} \right]$ 
D)  $\left[ \begin{array} { c c | c } 
1 & 6 & - 7 \
0 & 8 & 5
\end{array} \right]$ 
E)  $\left[ \begin{array} { c c | c } 
1 & 6 & - 7 \
0 & 0 & 0
\end{array} \right]$ 
A)  $\left[ \begin{array} { c c | c } 
1 & 6 & - 7 \
0 & 3 & 0
\end{array} \right]$ 
B)  $\left[ \begin{array} { c c | c } 
1 & 6 & - 7 \
0 & 0 & 5
\end{array} \right]$ 
C)  $\left[ \begin{array} { c c | c } 
1 & 6 & - 7 \
0 & 8 & 0
\end{array} \right]$ 
D)  $\left[ \begin{array} { c c | c } 
1 & 6 & - 7 \
0 & 8 & 5
\end{array} \right]$ 
E)  $\left[ \begin{array} { c c | c } 
1 & 6 & - 7 \
0 & 0 & 0
\end{array} \right]$

Use the graphs in the illustration to solve the equation. $- x - 4 = 2 x - 1$

Refer to the illustration. Answer the questions. How many solutions does the system of equations have? Are the equations dependent or independent?

Which matrix indicates that the equations of its associated system of equations has infinitely many solutions?

Evaluate the determinant $\left| \begin{array} { l l } 9 & - 3 \\0 & - 4\end{array} \right|$

A total of $25,000 was invested in two accounts for one year and the amount earned was $1,550. Part of the money was invested at 6% and the rest at 7%. Write a system of two equations in two unknowns that would model the situation. Let x = amount invested at 6% and y = amount invested at 7%.

Find the x -coordinate of the solution of the following system. Use the method of elimination. $( - 5 + 3 i ) - ( 3 - i )$

Solve the system. Give your answer as an ordered triple in the form of ( a, b, c ). $\left\{ \begin{array} { l } 2 a + 3 b - 2 c = 18 \\5 a - 6 b + c = 15 \\4 b - 2 c - 6 = 0\end{array} \right.$

Use the method of substitution to find the x -coordinate of the solution of the following system of equations. $a + b i$

An artist makes three types of ceramic statues at a monthly cost of $650 for 165 statues. The manufacturing costs for the three types are $5, $4, and $3. If the statues sell for $20, $12, and $9, respectively, how many of each type should be made to produce $2,100 in monthly revenue?

Determine whether the ordered pair $\left( \frac { 1 } { 3 } , \frac { 1 } { 2 } \right)$ is a solution of the following system. $\left\{ \begin{array} { c } 6 x - 8 y = - 2 \\- 6 x + 10 y = 3\end{array} \right.$

Find the equation of the form $y = a x ^ { 2 } + b x + c$ for the parabola shown in the illustration. $Find the equation of the form y = a x ^ { 2 } + b x + c for the parabola shown in the illustration.$

Find the augmented matrix that represents the system of $\left\{ \begin{array} { l } 7 x - 9 y = 3 \\7 x - 4 = 7 y\end{array} \right.$ .

Use Cramer s Rule to solve the system for z. $\left\{ \begin{array} { l } x + y - z = 4 \\8 x - 6 y + 7 z = 1 \\x + 9 y - z = - 2\end{array} \right.$

Solve the system by substitution, if possible. If the equations of the system are dependent, or if the system is inconsistent, so indicate. $i$

The graph of the equation $5 x + 8 y + 7 z = 6$ is a flat surface called a __________.

When we add the two equations of the system $\log _ { 5 } ( 2 x - 7 ) = \log _ { 5 } ( x + 1 )$ , the y -terms are __________.

Solve the system $\left\{ \begin{array} { l } x - 6 y = 9 \\4 x - 5 y = 17\end{array} \right.$ by matrices.

Which matrix shown below indicates that the equations of its associated system are dependent?

A Review of Basic Algebra

Graphs, Equations of Lines, and Functions

Inequalities

Exponents, Polynomials, and Polynomial Functions

Rational Expression and Equations

Radical Expressions and Equations

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conic Sections; More Graphing

Miscellaneous Topics

Filters

Exam 3: Systems of Equations

Use the graphs in the illustration to solve the equation. −x−4=2x−1- x - 4 = 2 x - 1−x−4=2x−1

Refer to the illustration. Answer the questions. How many solutions does the system of equations have? Are the equations dependent or independent?

Which matrix indicates that the equations of its associated system of equations has infinitely many solutions?

Evaluate the determinant ∣9−30−4∣\left| \begin{array} { l l } 9 & - 3 \\0 & - 4\end{array} \right|​90​−3−4​​

A total of $25,000 was invested in two accounts for one year and the amount earned was $1,550. Part of the money was invested at 6% and the rest at 7%. Write a system of two equations in two unknowns that would model the situation. Let x = amount invested at 6% and y = amount invested at 7%.

Find the x -coordinate of the solution of the following system. Use the method of elimination. (−5+3i)−(3−i)( - 5 + 3 i ) - ( 3 - i )(−5+3i)−(3−i)

Solve the system. Give your answer as an ordered triple in the form of ( a, b, c ). {2a+3b−2c=185a−6b+c=154b−2c−6=0\left\{ \begin{array} { l } 2 a + 3 b - 2 c = 18 \\5 a - 6 b + c = 15 \\4 b - 2 c - 6 = 0\end{array} \right.⎩⎨⎧​2a+3b−2c=185a−6b+c=154b−2c−6=0​

Use the method of substitution to find the x -coordinate of the solution of the following system of equations. a+bia + b ia+bi

An artist makes three types of ceramic statues at a monthly cost of $650 for 165 statues. The manufacturing costs for the three types are $5, $4, and $3. If the statues sell for $20, $12, and $9, respectively, how many of each type should be made to produce $2,100 in monthly revenue?

Determine whether the ordered pair (13,12)\left( \frac { 1 } { 3 } , \frac { 1 } { 2 } \right)(31​,21​) is a solution of the following system. {6x−8y=−2−6x+10y=3\left\{ \begin{array} { c } 6 x - 8 y = - 2 \\- 6 x + 10 y = 3\end{array} \right.{6x−8y=−2−6x+10y=3​

Find the equation of the form y=ax2+bx+cy = a x ^ { 2 } + b x + cy=ax2+bx+c for the parabola shown in the illustration.

Find the augmented matrix that represents the system of {7x−9y=37x−4=7y\left\{ \begin{array} { l } 7 x - 9 y = 3 \\7 x - 4 = 7 y\end{array} \right.{7x−9y=37x−4=7y​ .

Use Cramer s Rule to solve the system for z. {x+y−z=48x−6y+7z=1x+9y−z=−2\left\{ \begin{array} { l } x + y - z = 4 \\8 x - 6 y + 7 z = 1 \\x + 9 y - z = - 2\end{array} \right.⎩⎨⎧​x+y−z=48x−6y+7z=1x+9y−z=−2​

Solve the system by substitution, if possible. If the equations of the system are dependent, or if the system is inconsistent, so indicate. iii

The graph of the equation 5x+8y+7z=65 x + 8 y + 7 z = 65x+8y+7z=6 is a flat surface called a __________.

When we add the two equations of the system log⁡5(2x−7)=log⁡5(x+1)\log _ { 5 } ( 2 x - 7 ) = \log _ { 5 } ( x + 1 )log5​(2x−7)=log5​(x+1) , the y -terms are __________.

Solve the system {x−6y=94x−5y=17\left\{ \begin{array} { l } x - 6 y = 9 \\4 x - 5 y = 17\end{array} \right.{x−6y=94x−5y=17​ by matrices.

Which matrix shown below indicates that the equations of its associated system are dependent?

A Review of Basic Algebra

Graphs, Equations of Lines, and Functions

Inequalities

Exponents, Polynomials, and Polynomial Functions

Rational Expression and Equations

Radical Expressions and Equations

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conic Sections; More Graphing

Miscellaneous Topics

Filters

Use the graphs in the illustration to solve the equation. $- x - 4 = 2 x - 1$

Evaluate the determinant $\left| \begin{array} { l l } 9 & - 3 \\0 & - 4\end{array} \right|$

Find the x -coordinate of the solution of the following system. Use the method of elimination. $( - 5 + 3 i ) - ( 3 - i )$

Solve the system. Give your answer as an ordered triple in the form of ( a, b, c ). $\left\{ \begin{array} { l } 2 a + 3 b - 2 c = 18 \\5 a - 6 b + c = 15 \\4 b - 2 c - 6 = 0\end{array} \right.$

Use the method of substitution to find the x -coordinate of the solution of the following system of equations. $a + b i$

Determine whether the ordered pair $\left( \frac { 1 } { 3 } , \frac { 1 } { 2 } \right)$ is a solution of the following system. $\left\{ \begin{array} { c } 6 x - 8 y = - 2 \\- 6 x + 10 y = 3\end{array} \right.$

Find the equation of the form $y = a x ^ { 2 } + b x + c$ for the parabola shown in the illustration. $Find the equation of the form y = a x ^ { 2 } + b x + c for the parabola shown in the illustration.$

Find the augmented matrix that represents the system of $\left\{ \begin{array} { l } 7 x - 9 y = 3 \\7 x - 4 = 7 y\end{array} \right.$ .

Use Cramer s Rule to solve the system for z. $\left\{ \begin{array} { l } x + y - z = 4 \\8 x - 6 y + 7 z = 1 \\x + 9 y - z = - 2\end{array} \right.$

Solve the system by substitution, if possible. If the equations of the system are dependent, or if the system is inconsistent, so indicate. $i$

The graph of the equation $5 x + 8 y + 7 z = 6$ is a flat surface called a __________.

When we add the two equations of the system $\log _ { 5 } ( 2 x - 7 ) = \log _ { 5 } ( x + 1 )$ , the y -terms are __________.

Solve the system $\left\{ \begin{array} { l } x - 6 y = 9 \\4 x - 5 y = 17\end{array} \right.$ by matrices.