Question 1

Solve the system by using the inverse of the coefficient matrix.
-$x-y+z=3$
$x+y+z=1$
$\mathrm{x}+\mathrm{y}-\mathrm{z}=-7$

Accepted Answer

A)  $(-2,-1,4)$ 
B)  $(-2,4,-1)$ 
C)  $(4,-2,-1)$ 
D)  No solution 
A)  $(-2,-1,4)$ 
B)  $(-2,4,-1)$ 
C)  $(4,-2,-1)$ 
D)  No solution

Question 2

Given the matrices $A$ and $B$, find the matrix product $A B$.
-$\mathrm{A}=\left[\begin{array}{rr}0 & -3 \ 5 & 3\end{array}\right], \mathrm{B}=\left[\begin{array}{ll}-2 & 0 \ -1 & 1\end{array}\right]$ Find $\mathrm{AB}$.

Accepted Answer

A) $\left[\begin{array}{rr}-10 & -6 \ 5 & 6\end{array}\right]$ 
B) $\left[\begin{array}{rr}-3 & 3 \ -7 & -13\end{array}\right]$ 
C) $\left[\begin{array}{rr}0 & 6 \ -5 & 3\end{array}\right]$ 
D) $\left[\begin{array}{rr}3 & -3 \ -13 & 3\end{array}\right]$ 
A) $\left[\begin{array}{rr}-10 & -6 \ 5 & 6\end{array}\right]$ 
B) $\left[\begin{array}{rr}-3 & 3 \ -7 & -13\end{array}\right]$ 
C) $\left[\begin{array}{rr}0 & 6 \ -5 & 3\end{array}\right]$ 
D) $\left[\begin{array}{rr}3 & -3 \ -13 & 3\end{array}\right]$

Question 3

Solve the system of two equations in two variables.
-$5 x+9 y=43$
$-2 x-7 y=-24$

Accepted Answer

A)  $(5,3)$ 
B)  $(4,3)$ 
C)  $(5,2)$ 
D)  No solution 
A)  $(5,3)$ 
B)  $(4,3)$ 
C)  $(5,2)$ 
D)  No solution

Question 4

The diagram shows the roads connecting four cities. Write a matrix to represent the number of routes between each pair of cities without passing through another city.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 5

Solve the problem by writing and solving a suitable system of equations.
-Alan invests a total of $\$ 18,000$ in three different ways. He invests one part in a mutual fund which in the first year has a return of $11 \%$. He invests the second part in a government bond at $7 \%$ per year. The third part he puts in the bank at $5 \%$ per year. He invests twice as much in the mutual fund as in the bank. The first year Alan's investments bring a total return of $\$ 1500$. How much did he invest in each way?

Accepted Answer

A) m utual fund: $\$ 7400$; bond: $\$ 6900$ : bank: $\$ 3700$ 
B) m utual fund: $\$ 8000$; bond: $\$ 6000$ : bank: $\$ 4000$ 
C) m utual fund: $\$ 8000$; bond: $\$ 7000$ : bank: $\$ 4000$ 
D) m utual fund: $\$ 8600$; bond: $\$ 5100$ : bank: $\$ 4300$ 
A) m utual fund: $\$ 7400$; bond: $\$ 6900$ : bank: $\$ 3700$ 
B) m utual fund: $\$ 8000$; bond: $\$ 6000$ : bank: $\$ 4000$ 
C) m utual fund: $\$ 8000$; bond: $\$ 7000$ : bank: $\$ 4000$ 
D) m utual fund: $\$ 8600$; bond: $\$ 5100$ : bank: $\$ 4300$

Question 6

Write an augmented matrix for the system of equations.
-$9 x+9 z=54$
$-2 y+8 z=2$
$7 x+7 y+3 z=83$

Accepted Answer

A) 
$\left[\begin{array}{rrr|r}9 & 0 & 9 & 54 \ 0 & -2 & 8 & 2 \ 7 & 7 & 3 & 83\end{array}\right]$ 
B)  $\left[\begin{array}{rrr}9 & 0 & 9 \ 0 & -2 & 8 \ 7 & 7 & 3\end{array}\right]$ 
C) 
$\left[\begin{array}{rrr|r}9 & 0 & 7 & 54 \ 0 & -2 & 7 & 2 \ 9 & 8 & 3 & 83\end{array}\right]$ 
D) 
$\left[\begin{array}{rrr|r}9 & 9 & 0 & 54 \ -2 & 8 & 0 & 2 \ 7 & 7 & 3 & 83\end{array}\right]$ 
A) 
$\left[\begin{array}{rrr|r}9 & 0 & 9 & 54 \ 0 & -2 & 8 & 2 \ 7 & 7 & 3 & 83\end{array}\right]$ 
B)  $\left[\begin{array}{rrr}9 & 0 & 9 \ 0 & -2 & 8 \ 7 & 7 & 3\end{array}\right]$ 
C) 
$\left[\begin{array}{rrr|r}9 & 0 & 7 & 54 \ 0 & -2 & 7 & 2 \ 9 & 8 & 3 & 83\end{array}\right]$ 
D) 
$\left[\begin{array}{rrr|r}9 & 9 & 0 & 54 \ -2 & 8 & 0 & 2 \ 7 & 7 & 3 & 83\end{array}\right]$

Question 7

Write a system of equations and use the inverse of the coefficient matrix to solve the system.
-A company makes 3 types of cable. Cable A requires 3 black, 3 white, and 2 red wires. Cable B requires 1 black, 2 white, and 1 red wires. Cable $C$ requires 2 black, 1 white, and 2 red wires. They used 100 black, 110 white and 80 red wires. How many of each cable were made?

Accepted Answer

A) 10 cable A
83 cable B
20 cable C 
B) 20 cable A
20 cable B
10 cable C 
C)  20 cable A
20 cable B
83 cable C 
D)  20 cable A
93 cable B
10 cable C 
A) 10 cable A
83 cable B
20 cable C 
B) 20 cable A
20 cable B
10 cable C 
C)  20 cable A
20 cable B
83 cable C 
D)  20 cable A
93 cable B
10 cable C

Question 8

Given the matrices $A$ and $B$, find the matrix product $A B$.
-$\mathrm{A}=\left[\begin{array}{rr}-1 & 3 \ 5 & 2\end{array}\right], \mathrm{B}=\left[\begin{array}{lll}0 & -2 & 5 \ 1 & -3 & 2\end{array}\right]$ Find $\mathrm{AB}$.

Accepted Answer

A) $$\left[\begin{array}{ccc}
3 & -7 & 1 \
2 & -16 & 29
\end{array}\right]$$ 
B)  $A B$ is not defined. 
C) $$\left[\begin{array}{rrr}
3 & 2 & -7 \
-16 & 1 & 29
\end{array}\right]$$ 
D) $\left[\begin{array}{rr}0 & -6 \ 15 & 5 \ -6 & 4\end{array}\right]$ 
A) $$\left[\begin{array}{ccc}
3 & -7 & 1 \
2 & -16 & 29
\end{array}\right]$$ 
B)  $A B$ is not defined. 
C) $$\left[\begin{array}{rrr}
3 & 2 & -7 \
-16 & 1 & 29
\end{array}\right]$$ 
D) $\left[\begin{array}{rr}0 & -6 \ 15 & 5 \ -6 & 4\end{array}\right]$

Question 9

Solve the system by using the inverse of the coefficient matrix.
-$8 x+7 z=107$
$4 x+5 y+3 z=81$
$7 \mathrm{x}-3 \mathrm{y}=45$

Accepted Answer

A)  $(10,4,5)$ 
B)  $(9,-6,-5)$ 
C)  $(6,5,6)$ 
D)  $(9,6,5)$ 
A)  $(10,4,5)$ 
B)  $(9,-6,-5)$ 
C)  $(6,5,6)$ 
D)  $(9,6,5)$

Question 10

Use the Gauss-Jordan method to solve the system of equations.
-$x+y+z=-12$
$x-y+3 z=-8$
$4 x+y+z=-24$

Accepted Answer

A)  $(-4,-5,-3)$ 
B)  No solution 
C)  $(-3,-4,-5)$ 
D)  $(-3,-5,-4)$ 
A)  $(-4,-5,-3)$ 
B)  No solution 
C)  $(-3,-4,-5)$ 
D)  $(-3,-5,-4)$

Question 11

Solve the problem.
-The profits (in millions of dollars) of a company can be described by the equation $P(x)=a x^{2}+b x+c$, where $x$ is the number of years since 2000 . Profits were $\$ 7.7$ million in the year 2000, $\$ 9.3$ million in 2004, and $\$ 12.9$ million in 2008 . Find the values of $a, b$, and $c$ and use your answer to estimate profits in the year 2014. Round to the nearest tenth.

Accepted Answer

A) $\$23$ million 
B)  $\$ 22.1$ million 
C)  $\$ 23.6$ million 
D)  $\$ 13.6$ million 
A) $\$23$ million 
B)  $\$ 22.1$ million 
C)  $\$ 23.6$ million 
D)  $\$ 13.6$ million

Question 12

Perform row operations on the augmented matrix as far as necessary to determine whether the system is independent,dependent, or inconsistent.
-$x-y+4 z=4$
$4 \mathrm{x}+\mathrm{z}=2$
$x+4 y+z=18$

Accepted Answer

A)  Dependent 
B)  Inconsistent 
C)  Independent 
A)  Dependent 
B)  Inconsistent 
C)  Independent

Question 13

Write the word or phrase that best completes each statement or answers thequestion.
-A simplified economy is based on agriculture, manufacturing, and transportation. Each unit of agricultural output requires 0.3 unit of its own output, 0.5 of manufacturing, and 0.2 unit of transportation output. Each unit of manufacturing output requires 0.3 unit of its own output, 0.1 of agricultural, and 0.4 unit of transportation output. Each unit of transportation output requires 0.4 unit of its own output, 0.2 of agricultural, and 0.1 of manufacturing output. There is demand for 40 units of agricultural, 60 units of manufacturing, and 30 units of transportation output. How many units should each segment of the economy produce?

Accepted Answer

Agriculture: 269; Ma

Question 14

If $A$ is a $3 \times 3$ matrix and $A+B=$ is the $3 \times 3$ zero matrix, what can you say about the matrix?

Accepted Answer

A)  B is the $3 \times 3$ zero matrix 
B)  $\mathrm{B}=-\mathrm{A}$ 
C)  B is the $3 \times 3$ identity matrix 
D)  $B=A$ 
A)  B is the $3 \times 3$ zero matrix 
B)  $\mathrm{B}=-\mathrm{A}$ 
C)  B is the $3 \times 3$ identity matrix 
D)  $B=A$

Question 15

Solve the matrix equation for $X$.}
-$\mathrm{A}=\left[\begin{array}{rr}0 & -3 \ 2 & 2\end{array}\right], \mathrm{B}=\left[\begin{array}{rr}3 & -3 \ -6 & 2\end{array}\right], \mathrm{AX}=\mathrm{B}$

Accepted Answer

A) $\left[\begin{array}{rr}0 & 6 \ -2 & 2\end{array}\right]$ 
B) $\left[\begin{array}{ll}-2 & 0 \ -1 & 1\end{array}\right]$ 
C) $\left[\begin{array}{rr}-3 & -1 \ 2 & 0\end{array}\right]$ 
D) $\left[\begin{array}{rr}-4 & -4 \ 2 & 5\end{array}\right]$ 
A) $\left[\begin{array}{rr}0 & 6 \ -2 & 2\end{array}\right]$ 
B) $\left[\begin{array}{ll}-2 & 0 \ -1 & 1\end{array}\right]$ 
C) $\left[\begin{array}{rr}-3 & -1 \ 2 & 0\end{array}\right]$ 
D) $\left[\begin{array}{rr}-4 & -4 \ 2 & 5\end{array}\right]$

Question 16

What is the size of the matrix?
$\left[\begin{array}{rrr}5 & 5 & 6 \ -4 & 2 & 1\end{array}\right]$

Accepted Answer

A)  6 
B)  $2 \times 3$ 
C)  $3 \times 2$ 
D)  3 
A)  6 
B)  $2 \times 3$ 
C)  $3 \times 2$ 
D)  3

Question 17

Solve the system by using the inverse of the coefficient matrix.
-$9 x+4 y-z=64$
$x-2 y+2 z=3$
$-5 x+y+z=-14$

Accepted Answer

A)  $(6,4,5)$ 
B)  $(6,5,6)$ 
C)  $(5,-6,-5)$ 
D)  $(5,6,5)$ 
A)  $(6,4,5)$ 
B)  $(6,5,6)$ 
C)  $(5,-6,-5)$ 
D)  $(5,6,5)$

Question 18

Perform row operations on the augmented matrix as far as necessary to determine whether the system is independent,dependent, or inconsistent.
-$x+y-2 z=8$
$3 x+z=-6$
$2 x-y+3 z=-14$

Accepted Answer

A)  Independent 
B)  Inconsistent 
C)  Dependent 
A)  Independent 
B)  Inconsistent 
C)  Dependent

Question 19

Perform the row operations on the matrix and write the resulting matrix.
-Replace $R_{2}$ by $R_{1}+(-1) R_{2}$
$\left[\begin{array}{rr|r}1 & -3 & 4 \ 2 & 3 & 1\end{array}\right]$

Accepted Answer

A) 
$\left[\begin{array}{rr|r}1 & -2 & 2 \ 3 & 1 & 3\end{array}\right]$ 
B) 
$\left[\begin{array}{rr|r}1 & -2 & 2 \ 1 & 5 & -1\end{array}\right]$ 
C) 
$\left[\begin{array}{rr|r}1 & -3 & 4 \ -1 & -6 & 3\end{array}\right]$ 
D) 
$\left[\begin{array}{rr|r}1 & -2 & 2 \ 2 & 3 & 1\end{array}\right]$ 
A) 
$\left[\begin{array}{rr|r}1 & -2 & 2 \ 3 & 1 & 3\end{array}\right]$ 
B) 
$\left[\begin{array}{rr|r}1 & -2 & 2 \ 1 & 5 & -1\end{array}\right]$ 
C) 
$\left[\begin{array}{rr|r}1 & -3 & 4 \ -1 & -6 & 3\end{array}\right]$ 
D) 
$\left[\begin{array}{rr|r}1 & -2 & 2 \ 2 & 3 & 1\end{array}\right]$

Question 20

Multiply both sides of each equation by a common denominator to eliminate the fractions. Then solve the system.
-$\frac{3 x}{2}-\frac{y}{3}=-18$
$\frac{3 x}{4}+\frac{2 y}{9}=-9$

Accepted Answer

A)  $(0,-12)$ 
B)  $(-12,0)$ 
C)  $(0,12)$ 
D)  $(12,0)$ 
A)  $(0,-12)$ 
B)  $(-12,0)$ 
C)  $(0,12)$ 
D)  $(12,0)$

Solve the system by using the inverse of the coefficient matrix. - $x-y+z=3$ $x+y+z=1$ $\mathrm{x}+\mathrm{y}-\mathrm{z}=-7$

Given the matrices $A$ and $B$ , find the matrix product $A B$ . - $\mathrm{A}=\left[\begin{array}{rr}0 & -3 \\ 5 & 3\end{array}\right], \mathrm{B}=\left[\begin{array}{ll}-2 & 0 \\ -1 & 1\end{array}\right]$ Find $\mathrm{AB}$ .

Solve the system of two equations in two variables. - $5 x+9 y=43$ $-2 x-7 y=-24$

The diagram shows the roads connecting four cities. Write a matrix to represent the number of routes between each pair of cities without passing through another city.

Write an augmented matrix for the system of equations. - $9 x+9 z=54$ $-2 y+8 z=2$ $7 x+7 y+3 z=83$

Given the matrices $A$ and $B$ , find the matrix product $A B$ . - $\mathrm{A}=\left[\begin{array}{rr}-1 & 3 \\ 5 & 2\end{array}\right], \mathrm{B}=\left[\begin{array}{lll}0 & -2 & 5 \\ 1 & -3 & 2\end{array}\right]$ Find $\mathrm{AB}$ .

Solve the system by using the inverse of the coefficient matrix. - $8 x+7 z=107$ $4 x+5 y+3 z=81$ $7 \mathrm{x}-3 \mathrm{y}=45$

Use the Gauss-Jordan method to solve the system of equations. - $x+y+z=-12$ $x-y+3 z=-8$ $4 x+y+z=-24$

Perform row operations on the augmented matrix as far as necessary to determine whether the system is independent,dependent, or inconsistent. - $x-y+4 z=4$ $4 \mathrm{x}+\mathrm{z}=2$ $x+4 y+z=18$

If $A$ is a $3 \times 3$ matrix and $A+B=$ is the $3 \times 3$ zero matrix, what can you say about the matrix?

Solve the matrix equation for $X$ .} - $\mathrm{A}=\left[\begin{array}{rr}0 & -3 \\ 2 & 2\end{array}\right], \mathrm{B}=\left[\begin{array}{rr}3 & -3 \\ -6 & 2\end{array}\right], \mathrm{AX}=\mathrm{B}$

What is the size of the matrix? $\left[\begin{array}{rrr}5 & 5 & 6 \\ -4 & 2 & 1\end{array}\right]$

Solve the system by using the inverse of the coefficient matrix. - $9 x+4 y-z=64$ $x-2 y+2 z=3$ $-5 x+y+z=-14$

Perform row operations on the augmented matrix as far as necessary to determine whether the system is independent,dependent, or inconsistent. - $x+y-2 z=8$ $3 x+z=-6$ $2 x-y+3 z=-14$

Perform the row operations on the matrix and write the resulting matrix. -Replace $R_{2}$ by $R_{1}+(-1) R_{2}$ $\left[\begin{array}{rr|r}1 & -3 & 4 \\ 2 & 3 & 1\end{array}\right]$

Multiply both sides of each equation by a common denominator to eliminate the fractions. Then solve the system. - $\frac{3 x}{2}-\frac{y}{3}=-18$ $\frac{3 x}{4}+\frac{2 y}{9}=-9$

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Exam 6: Systems of Linear Equations and Matrices

Solve the system by using the inverse of the coefficient matrix. - x−y+z=3x-y+z=3x−y+z=3 x+y+z=1x+y+z=1x+y+z=1 x+y−z=−7\mathrm{x}+\mathrm{y}-\mathrm{z}=-7x+y−z=−7

Given the matrices AAA and BBB , find the matrix product ABA BAB . - A=[0−353],B=[−20−11]\mathrm{A}=\left[\begin{array}{rr}0 & -3 \\ 5 & 3\end{array}\right], \mathrm{B}=\left[\begin{array}{ll}-2 & 0 \\ -1 & 1\end{array}\right]A=[05​−33​],B=[−2−1​01​] Find AB\mathrm{AB}AB .

Solve the system of two equations in two variables. - 5x+9y=435 x+9 y=435x+9y=43 −2x−7y=−24-2 x-7 y=-24−2x−7y=−24

The diagram shows the roads connecting four cities. Write a matrix to represent the number of routes between each pair of cities without passing through another city.

Write an augmented matrix for the system of equations. - 9x+9z=549 x+9 z=549x+9z=54 −2y+8z=2-2 y+8 z=2−2y+8z=2 7x+7y+3z=837 x+7 y+3 z=837x+7y+3z=83

Solve the system by using the inverse of the coefficient matrix. - 8x+7z=1078 x+7 z=1078x+7z=107 4x+5y+3z=814 x+5 y+3 z=814x+5y+3z=81 7x−3y=457 \mathrm{x}-3 \mathrm{y}=457x−3y=45

Use the Gauss-Jordan method to solve the system of equations. - x+y+z=−12x+y+z=-12x+y+z=−12 x−y+3z=−8x-y+3 z=-8x−y+3z=−8 4x+y+z=−244 x+y+z=-244x+y+z=−24

Perform row operations on the augmented matrix as far as necessary to determine whether the system is independent,dependent, or inconsistent. - x−y+4z=4x-y+4 z=4x−y+4z=4 4x+z=24 \mathrm{x}+\mathrm{z}=24x+z=2 x+4y+z=18x+4 y+z=18x+4y+z=18

If AAA is a 3×33 \times 33×3 matrix and A+B=A+B=A+B= is the 3×33 \times 33×3 zero matrix, what can you say about the matrix?

Solve the matrix equation for XXX .} - A=[0−322],B=[3−3−62],AX=B\mathrm{A}=\left[\begin{array}{rr}0 & -3 \\ 2 & 2\end{array}\right], \mathrm{B}=\left[\begin{array}{rr}3 & -3 \\ -6 & 2\end{array}\right], \mathrm{AX}=\mathrm{B}A=[02​−32​],B=[3−6​−32​],AX=B

What is the size of the matrix? [556−421]\left[\begin{array}{rrr}5 & 5 & 6 \\ -4 & 2 & 1\end{array}\right][5−4​52​61​]

Solve the system by using the inverse of the coefficient matrix. - 9x+4y−z=649 x+4 y-z=649x+4y−z=64 x−2y+2z=3x-2 y+2 z=3x−2y+2z=3 −5x+y+z=−14-5 x+y+z=-14−5x+y+z=−14

Perform row operations on the augmented matrix as far as necessary to determine whether the system is independent,dependent, or inconsistent. - x+y−2z=8x+y-2 z=8x+y−2z=8 3x+z=−63 x+z=-63x+z=−6 2x−y+3z=−142 x-y+3 z=-142x−y+3z=−14

Perform the row operations on the matrix and write the resulting matrix. -Replace R2R_{2}R2​ by R1+(−1)R2R_{1}+(-1) R_{2}R1​+(−1)R2​ [1−34231]\left[\begin{array}{rr|r}1 & -3 & 4 \\ 2 & 3 & 1\end{array}\right][12​−33​41​]

Multiply both sides of each equation by a common denominator to eliminate the fractions. Then solve the system. - 3x2−y3=−18\frac{3 x}{2}-\frac{y}{3}=-1823x​−3y​=−18 3x4+2y9=−9\frac{3 x}{4}+\frac{2 y}{9}=-943x​+92y​=−9

Algebra and Equations

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Functions and Graphs

Exponential and Logarithmic Functions

Mathematics of Finance

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Counting, Probability Distributions, and Further Topics in Probability

Introduction to Statistics

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Integral Calculus

Multivariate Calculus

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Solve the system by using the inverse of the coefficient matrix. - $x-y+z=3$ $x+y+z=1$ $\mathrm{x}+\mathrm{y}-\mathrm{z}=-7$

Given the matrices $A$ and $B$ , find the matrix product $A B$ . - $\mathrm{A}=\left[\begin{array}{rr}0 & -3 \\ 5 & 3\end{array}\right], \mathrm{B}=\left[\begin{array}{ll}-2 & 0 \\ -1 & 1\end{array}\right]$ Find $\mathrm{AB}$ .

Solve the system of two equations in two variables. - $5 x+9 y=43$ $-2 x-7 y=-24$

Write an augmented matrix for the system of equations. - $9 x+9 z=54$ $-2 y+8 z=2$ $7 x+7 y+3 z=83$

Solve the system by using the inverse of the coefficient matrix. - $8 x+7 z=107$ $4 x+5 y+3 z=81$ $7 \mathrm{x}-3 \mathrm{y}=45$

Use the Gauss-Jordan method to solve the system of equations. - $x+y+z=-12$ $x-y+3 z=-8$ $4 x+y+z=-24$

Perform row operations on the augmented matrix as far as necessary to determine whether the system is independent,dependent, or inconsistent. - $x-y+4 z=4$ $4 \mathrm{x}+\mathrm{z}=2$ $x+4 y+z=18$

If $A$ is a $3 \times 3$ matrix and $A+B=$ is the $3 \times 3$ zero matrix, what can you say about the matrix?

Solve the matrix equation for $X$ .} - $\mathrm{A}=\left[\begin{array}{rr}0 & -3 \\ 2 & 2\end{array}\right], \mathrm{B}=\left[\begin{array}{rr}3 & -3 \\ -6 & 2\end{array}\right], \mathrm{AX}=\mathrm{B}$

What is the size of the matrix? $\left[\begin{array}{rrr}5 & 5 & 6 \\ -4 & 2 & 1\end{array}\right]$

Solve the system by using the inverse of the coefficient matrix. - $9 x+4 y-z=64$ $x-2 y+2 z=3$ $-5 x+y+z=-14$

Perform row operations on the augmented matrix as far as necessary to determine whether the system is independent,dependent, or inconsistent. - $x+y-2 z=8$ $3 x+z=-6$ $2 x-y+3 z=-14$

Perform the row operations on the matrix and write the resulting matrix. -Replace $R_{2}$ by $R_{1}+(-1) R_{2}$ $\left[\begin{array}{rr|r}1 & -3 & 4 \\ 2 & 3 & 1\end{array}\right]$

Multiply both sides of each equation by a common denominator to eliminate the fractions. Then solve the system. - $\frac{3 x}{2}-\frac{y}{3}=-18$ $\frac{3 x}{4}+\frac{2 y}{9}=-9$