Question 1

Use the properties of determinants to find the value of the second determinant, given the value of the first.
-$$\left| \begin{array} { c c c } 
x & y & z \
u & v & w \
1 & - 3 & 4
\end{array} \right| = - 138 \left| \begin{array} { c c c } 
x & y & z \
u & v & w \
2 & - 6 & 8
\end{array} \right| = ?$$ $$\begin{array} { c c c } 
x & y & z \
a & v & w \
1 & - 3 & 4
\end{array} | = - 138 | \begin{array} { c c c } 
x & y & z \
u & v & w \
2 & - 6 & 8
\end{array} \mid = ?$$

Accepted Answer

A)   -276
B)   -138
C)   276
D)   138  A

Question 2

Which method should be used to solve the system? Explain your answer, including a description of the first step. -7x² - 3y² = 36 5x + 5y = -5

Accepted Answer

Substitution should be used, because using elimination would mean introducing an xy term into the
second equation unnecessarily. The second equation should be solved for x or y.

Question 3

Which method should be used to solve the system? Explain your answer, including a description of the first step. -x² + 9y² = 9 7x² + 8y² = 81

Accepted Answer

Either method may be used. Elimination may be used since the equations have the same types of terms ( x² , y2, constant). If elimination is used, then the first equation should be multiplied by 7 or -7. Substitution may be used efficiently, since a coefficient of the first equation is 1. If substitution is used, then the first equation should be solved for x² .

Question 4

Find the inverse of the matrix.
-$A = \left[ \begin{array} { r r } 
14 & - 6 \
- 7 & 3
\end{array} \right]$

Accepted Answer

The answer of Find the inverse of the matrix.
-\(A =...

Question 5

Find the inverse of the matrix.
-$$\left[ \begin{array} { r r  } 
0  & -6\
-4   & 5 \
\end{array} \right]$$

Accepted Answer

A)   [0−14−16−524]\left[ \begin{array} { c c } 0 & - \frac { 1 } { 4 } \ - \frac { 1 } { 6 } & - \frac { 5 } { 24 } \end{array} ight][0−61​​−41​−245​​] 
B)    [−160−524−14]\left[ \begin{array} { c c } - \frac { 1 } { 6 } & 0 \ - \frac { 5 } { 24 } & - \frac { 1 } { 4 } \end{array} ight][−61​−245​​0−41​​] 
C)    [−52414−160]\left[ \begin{array} { c c } - \frac { 5 } { 24 } & \frac { 1 } { 4 } \ -\frac { 1 } { 6 } & 0 \end{array} ight][−245​−61​​41​0​] 
D)    [−52414160]\left[ \begin{array} { c c } - \frac { 5 } { 24 } & \frac { 1 } { 4 } \ \frac { 1 } { 6 } & 0 \end{array} ight][−245​61​​41​0​]

Question 6

Use a graphing utility to solve the system of equations. Express the solution rounded to two decimal places.
-$$\left\{ \begin{array} { r } 
x ^ { 3 } + y ^ { 2 } = 2 \
x ^ { 2 } y = 4
\end{array} \right.$$

Accepted Answer

A)    x=−1.37,y=2.14x = - 1.37 , y = 2.14x=−1.37,y=2.14 
B)    x=1.37,y=2.14x = 1.37 , y = 2.14x=1.37,y=2.14 
C)    x=2.14,y=1.37x = 2.14 , y = 1.37x=2.14,y=1.37 
D)    x=2.14,y=−1.37x = 2.14 , y = - 1.37x=2.14,y=−1.37

Question 7

Solve the system of equations using substitution.
-$\left\{ \begin{array} { l } \ln x = 3 \ln y \ 3 ^ { x } = 27 y \   \end{array} \right.$

Accepted Answer

A)    x=3,y=33x = \sqrt { 3 } , y = 3\sqrt { 3 }x=3c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z"/>​,y=33c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z"/>​ 
B)    x=9,y=3x = 9 , y = \sqrt { 3 }x=9,y=3c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z"/>​ 
C)    x=33,y=3x = 3 \sqrt { 3 } , y = \sqrt { 3 }x=33c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z"/>​,y=3c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z"/>​ 
D)    x=3,y=9x = \sqrt { 3 } , y = 9x=3c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z"/>​,y=9

Question 8

Find the inverse of the matrix.
-$$\left[ \begin{array} { c c c } 
2 & - 5 & 3 \
2 & - 4 & 8 \
4 & - 9 & 11
\end{array} \right]$$

Accepted Answer

A)    [1014015000]\left[ \begin{array} { l l l } 1 & 0 & 14 \ 0 & 1 & 5 \ 0 & 0 & 0 \end{array} ight]H403z M403 1759 V0 H319 V1759 v0 v1759 h84z"/>​100​010​1450​M347 1759 V0 H263 V1759 v0 v1759 h84z"/>​ 
B)   No inverse
C)    [10140150−10]\left[ \begin{array} { c c c } 1 & 0 & 14 \ 0 & 1 & 5 \ 0 & - 1 & 0 \end{array} ight]H403z M403 1759 V0 H319 V1759 v0 v1759 h84z"/>​100​01−1​1450​M347 1759 V0 H263 V1759 v0 v1759 h84z"/>​ 
D)    [224−5−4−93811]\left[ \begin{array} { c c c } 2 & 2 & 4 \ - 5 & - 4 & - 9 \ 3 & 8 & 11 \end{array} ight]H403z M403 1759 V0 H319 V1759 v0 v1759 h84z"/>​2−53​2−48​4−911​M347 1759 V0 H263 V1759 v0 v1759 h84z"/>​

Question 9

Which method should be used to solve the system? Explain your answer, including a description of the first step. -x² - y² = 16 x - 8y = -6

Accepted Answer

The answer of Which method should be used to solve...

Question 10

Solve the problem.
-A retired couple has $140,000 to invest to obtain annual income. They want some of it invested in safe Certificates of Deposit yielding 5%. The rest they want to invest in AA bonds yielding 12% per year. How much
Should they invest in each to realize exactly $13,300 per year?

Accepted Answer

A)   $90,000 at 5% and $50,000 at 12%
B)   $80,000 at 5% and $60,000 at 12%
C)   $90,000 at 12% and $50,000 at 5%
D)   $100,000 at 12% and $40,000 at 5%

Question 11

Tell whether the given rational expression is proper or improper.
-$$\frac { x ^ { 2 } - 12 x + 36 } { \left( x ^ { 2 } - 8 x + 15 \right) ( x + 3 ) }$$

Accepted Answer

A)   Proper
B)   Improper

Question 12

Use the properties of determinants to find the value of the second determinant, given the value of the first.
-$$\left| \begin{array} { c c c } 
x & y & z \
u & v & w \
1 & - 3 & - 4
\end{array} \right| = 62 \left| \begin{array} { c c c } 
1 & - 3 & - 4 \
3 u & 3 v & 3 w \
x - 1 & y + 3 & z + 4
\end{array} \right| = ?$$

Accepted Answer

A)   186
B)   -186
C)   62
D)   -62

Question 13

Solve the system of equations using substitution.
-$$\left\{ \begin{array} { l } 
x y - x ^ { 2 } = - 20 \
x - 2 y = 3
\end{array} \right.$$

Accepted Answer

A)    x=−5,y=−1;x=8,y=112x = - 5 , y = - 1 ; x = 8 , y = \frac { 11 } { 2 }x=−5,y=−1;x=8,y=211​ 
B)    x=−5,y=−1;x=112,y=8x = - 5 , y = - 1 ; x = \frac { 11 } { 2 } , y = 8x=−5,y=−1;x=211​,y=8 
C)    x=5,y=1;x=−8,y=−112x = 5 , y = 1 ; x = - 8 , y = - \frac { 11 } { 2 }x=5,y=1;x=−8,y=−211​ 
D)    x=5,y=1;x=−112,y=−8x = 5 , y = 1 ; x = - \frac { 11 } { 2 } , y = - 8x=5,y=1;x=−211​,y=−8

Question 14

Solve the system of equations by using substitution.
-$$\left\{ \begin{array} { c } 
x + 6 y = 6 \
4 x - 9 y = - 9
\end{array} \right.$$

Accepted Answer

A)   x = 0, y = 1
B)   x = 1, y = 1
C)   x = 1, y = 0
D)   x = 0, y = 0

Question 15

Write the partial fraction decomposition of the rational expression.
-$$\frac { 2 x - 5 } { x ^ { 2 } - 5 x - 6 }$$

Accepted Answer

A)    1x−6+1x+1\frac { 1 } { x - 6 } + \frac { 1 } { x + 1 }x−61​+x+11​ 
B)    1x−3+1x−2\frac { 1 } { x - 3 } + \frac { 1 } { x - 2 }x−31​+x−21​ 
C)    17x+6−3x−1\frac { 17 } { x + 6 } - \frac { 3 } { x - 1 }x+617​−x−13​ 
D)    9x+2+1x−3\frac { 9 } { x + 2 } + \frac { 1 } { x - 3 }x+29​+x−31​

Question 16

Graph the system of inequalities.
-

Accepted Answer

A)  
B)  
C)  
D)

Question 17

Solve the problem.
-The Family Arts Center charges $21 for adults, $13 for senior citizens, and $8 for children under 12 for their live performances on Sunday afternoon. This past Sunday, the paid revenue was $12,388 for 905 tickets sold. There
Were 50 more children than adults. How many children attended?

Accepted Answer

A)   291 children
B)   341 children
C)   273 children
D)   331 children

Question 18

Use a graphing utility to find the inverse of the matrix, if it exists. Round answers to two decimal places, if necessary.
-$$\left[ \begin{array} { r r r r } 
1 & - 4 & 0 & 0 \
0 & 1 & - 2 & 0 \
0 & 0 & 1 & - 1 \
0 & 0 & 0 & 1
\end{array} \right]$$

Accepted Answer

A)    [11−28012−800140001]\left[ \begin{array} { r r r r } 1 & 1 & - 2 & 8 \ 0 & 1 & 2 & - 8 \ 0 & 0 & 1 & 4 \ 0 & 0 & 0 & 1 \end{array} ight]H403z M403 1759 V0 H319 V1759 v1200 v1759 h84z"/>​1000​1100​−2210​8−841​M347 1759 V0 H263 V1759 v1200 v1759 h84z"/>​ 
B)    [1000410082104211]\left[ \begin{array} { l l l l } 1 & 0 & 0 & 0 \ 4 & 1 & 0 & 0 \ 8 & 2 & 1 & 0 \ 4 & 2 & 1 & 1 \end{array} ight]H403z M403 1759 V0 H319 V1759 v1200 v1759 h84z"/>​1484​0122​0011​0001​M347 1759 V0 H263 V1759 v1200 v1759 h84z"/>​ 
C)    [10001100−22108−841]\left[ \begin{array} { r r r r } 1 & 0 & 0 & 0 \ 1 & 1 & 0 & 0 \ - 2 & 2 & 1 & 0 \ 8 & - 8 & 4 & 1 \end{array} ight]H403z M403 1759 V0 H319 V1759 v1200 v1759 h84z"/>​11−28​012−8​0014​0001​M347 1759 V0 H263 V1759 v1200 v1759 h84z"/>​ 
D)    [1488012200110001]\left[ \begin{array} { l l l l } 1 & 4 & 8 & 8 \ 0 & 1 & 2 & 2 \ 0 & 0 & 1 & 1 \ 0 & 0 & 0 & 1 \end{array} ight]H403z M403 1759 V0 H319 V1759 v1200 v1759 h84z"/>​1000​4100​8210​8211​M347 1759 V0 H263 V1759 v1200 v1759 h84z"/>​

Question 19

Solve the system of equations using substitution.
-$$\left\{ \begin{array} { r } 
x y = 20 \
x + y = 9
\end{array} \right.$$

Accepted Answer

A)    x=20,y=1;x=1,y=20x = 20 , y = 1 ; x = 1 , y = 20x=20,y=1;x=1,y=20 
B)    x=10,y=2;x=2,y=10x = 10 , y = 2 ; x = 2 , y = 10x=10,y=2;x=2,y=10 
C)    x=6,y=3;x=3,y=6x = 6 , y = 3 ; x = 3 , y = 6x=6,y=3;x=3,y=6 
D)    x=5,y=4;x=4,y=5x = 5 , y = 4 ; x = 4 , y = 5x=5,y=4;x=4,y=5

Question 20

Graph the inequality.
-y ≤-3

Accepted Answer

A)  
B)  
C)  
D)

Exam 6: Systems of Equations and Inequalities

Which method should be used to solve the system? Explain your answer, including a description of the first step. -7x² - 3y² = 36 5x + 5y = -5

Which method should be used to solve the system? Explain your answer, including a description of the first step. -x² + 9y² = 9 7x² + 8y² = 81

Find the inverse of the matrix. - $A = \left[ \begin{array} { r r } 14 & - 6 \\- 7 & 3\end{array} \right]$

Find the inverse of the matrix. - $\left[ \begin{array} { r r } 0 & -6\\-4 & 5 \\\end{array} \right]$

Use a graphing utility to solve the system of equations. Express the solution rounded to two decimal places. - $\left\{ \begin{array} { r } x ^ { 3 } + y ^ { 2 } = 2 \\x ^ { 2 } y = 4\end{array} \right.$

Solve the system of equations using substitution. - $\left\{ \begin{array} { l } \ln x = 3 \ln y \\ 3 ^ { x } = 27 y \\ \end{array} \right.$

Find the inverse of the matrix. - $\left[ \begin{array} { c c c } 2 & - 5 & 3 \\2 & - 4 & 8 \\4 & - 9 & 11\end{array} \right]$

Which method should be used to solve the system? Explain your answer, including a description of the first step. -x² - y² = 16 x - 8y = -6

Solve the problem. -A retired couple has $140,000 to invest to obtain annual income. They want some of it invested in safe Certificates of Deposit yielding 5%. The rest they want to invest in AA bonds yielding 12% per year. How much Should they invest in each to realize exactly $13,300 per year?

Tell whether the given rational expression is proper or improper. - $\frac { x ^ { 2 } - 12 x + 36 } { \left( x ^ { 2 } - 8 x + 15 \right) ( x + 3 ) }$

Solve the system of equations using substitution. - $\left\{ \begin{array} { l } x y - x ^ { 2 } = - 20 \\x - 2 y = 3\end{array} \right.$

Solve the system of equations by using substitution. - $\left\{ \begin{array} { c } x + 6 y = 6 \\4 x - 9 y = - 9\end{array} \right.$

Write the partial fraction decomposition of the rational expression. - $\frac { 2 x - 5 } { x ^ { 2 } - 5 x - 6 }$

Graph the system of inequalities. -

Use a graphing utility to find the inverse of the matrix, if it exists. Round answers to two decimal places, if necessary. - $\left[ \begin{array} { r r r r } 1 & - 4 & 0 & 0 \\0 & 1 & - 2 & 0 \\0 & 0 & 1 & - 1 \\0 & 0 & 0 & 1\end{array} \right]$

Solve the system of equations using substitution. - $\left\{ \begin{array} { r } x y = 20 \\x + y = 9\end{array} \right.$

Graph the inequality. -y ≤-3

Exam 6: Systems of Equations and Inequalities

Which method should be used to solve the system? Explain your answer, including a description of the first step. -7x2 - 3y2 = 36 5x + 5y = -5

Which method should be used to solve the system? Explain your answer, including a description of the first step. -x2 + 9y2 = 9 7x2 + 8y2 = 81

Find the inverse of the matrix. - A=[14−6−73]A = \left[ \begin{array} { r r } 14 & - 6 \\- 7 & 3\end{array} \right]A=[14−7​−63​]

Find the inverse of the matrix. - [0−6−45]\left[ \begin{array} { r r } 0 & -6\\-4 & 5 \\\end{array} \right][0−4​−65​]

Use a graphing utility to solve the system of equations. Express the solution rounded to two decimal places. - {x3+y2=2x2y=4\left\{ \begin{array} { r } x ^ { 3 } + y ^ { 2 } = 2 \\x ^ { 2 } y = 4\end{array} \right.{x3+y2=2x2y=4​

Solve the system of equations using substitution. - {ln⁡x=3ln⁡y3x=27y\left\{ \begin{array} { l } \ln x = 3 \ln y \\ 3 ^ { x } = 27 y \\ \end{array} \right.{lnx=3lny3x=27y​

Find the inverse of the matrix. - [2−532−484−911]\left[ \begin{array} { c c c } 2 & - 5 & 3 \\2 & - 4 & 8 \\4 & - 9 & 11\end{array} \right]​224​−5−4−9​3811​​

Which method should be used to solve the system? Explain your answer, including a description of the first step. -x2 - y2 = 16 x - 8y = -6

Solve the problem. -A retired couple has $140,000 to invest to obtain annual income. They want some of it invested in safe Certificates of Deposit yielding 5%. The rest they want to invest in AA bonds yielding 12% per year. How much Should they invest in each to realize exactly $13,300 per year?

Tell whether the given rational expression is proper or improper. - x2−12x+36(x2−8x+15) (x+3) \frac { x ^ { 2 } - 12 x + 36 } { \left( x ^ { 2 } - 8 x + 15 \right) ( x + 3 ) }(x2−8x+15) (x+3) x2−12x+36​

Solve the system of equations using substitution. - {xy−x2=−20x−2y=3\left\{ \begin{array} { l } x y - x ^ { 2 } = - 20 \\x - 2 y = 3\end{array} \right.{xy−x2=−20x−2y=3​

Solve the system of equations by using substitution. - {x+6y=64x−9y=−9\left\{ \begin{array} { c } x + 6 y = 6 \\4 x - 9 y = - 9\end{array} \right.{x+6y=64x−9y=−9​

Write the partial fraction decomposition of the rational expression. - 2x−5x2−5x−6\frac { 2 x - 5 } { x ^ { 2 } - 5 x - 6 }x2−5x−62x−5​

Graph the system of inequalities. -

Solve the system of equations using substitution. - {xy=20x+y=9\left\{ \begin{array} { r } x y = 20 \\x + y = 9\end{array} \right.{xy=20x+y=9​

Graph the inequality. -y ≤-3

Which method should be used to solve the system? Explain your answer, including a description of the first step. -7x² - 3y² = 36 5x + 5y = -5

Which method should be used to solve the system? Explain your answer, including a description of the first step. -x² + 9y² = 9 7x² + 8y² = 81

Find the inverse of the matrix. - $A = \left[ \begin{array} { r r } 14 & - 6 \\- 7 & 3\end{array} \right]$

Find the inverse of the matrix. - $\left[ \begin{array} { r r } 0 & -6\\-4 & 5 \\\end{array} \right]$

Use a graphing utility to solve the system of equations. Express the solution rounded to two decimal places. - $\left\{ \begin{array} { r } x ^ { 3 } + y ^ { 2 } = 2 \\x ^ { 2 } y = 4\end{array} \right.$

Solve the system of equations using substitution. - $\left\{ \begin{array} { l } \ln x = 3 \ln y \\ 3 ^ { x } = 27 y \\ \end{array} \right.$

Find the inverse of the matrix. - $\left[ \begin{array} { c c c } 2 & - 5 & 3 \\2 & - 4 & 8 \\4 & - 9 & 11\end{array} \right]$

Which method should be used to solve the system? Explain your answer, including a description of the first step. -x² - y² = 16 x - 8y = -6

Tell whether the given rational expression is proper or improper. - $\frac { x ^ { 2 } - 12 x + 36 } { \left( x ^ { 2 } - 8 x + 15 \right) ( x + 3 ) }$

Solve the system of equations using substitution. - $\left\{ \begin{array} { l } x y - x ^ { 2 } = - 20 \\x - 2 y = 3\end{array} \right.$

Solve the system of equations by using substitution. - $\left\{ \begin{array} { c } x + 6 y = 6 \\4 x - 9 y = - 9\end{array} \right.$

Write the partial fraction decomposition of the rational expression. - $\frac { 2 x - 5 } { x ^ { 2 } - 5 x - 6 }$

Solve the system of equations using substitution. - $\left\{ \begin{array} { r } x y = 20 \\x + y = 9\end{array} \right.$