Question 1

Use a graphing calculator to approximate the solutions of the system. $$\left\{ \begin{array} { c } 
3.8 x + 3.9 y = 38.03 \
- 9 x + 4 y = 14.5
\end{array} \right.$$

Accepted Answer

A)  $\quad ( 7.9,1.9 )$ 
B)  $\quad ( - 6,10.8 )$ 
C)  $\quad ( - 1.9 , - 7.9 )$ 
D)  $\quad ( 1.9,7.9 )$ 
E)  $\quad ( 9.8 , - 5 )$ 
A)  $\quad ( 7.9,1.9 )$ 
B)  $\quad ( - 6,10.8 )$ 
C)  $\quad ( - 1.9 , - 7.9 )$ 
D)  $\quad ( 1.9,7.9 )$ 
E)  $\quad ( 9.8 , - 5 )$

Question 2

Two artists make winter yard ornaments.They get $83 for each wooden snowman they make and $74 for each wooden Santa Claus.On average, Nina must work 8 hours and Roberta 6 hours to make a
Snowman.Nina must work 4 hours and Roberta 8 hours to make a Santa Claus.If neither wishes to
Work more than 40 hours per week, how many of each ornament should they make each week to
Maximize their income? The information is summarized in the table below.

Accepted Answer

A)  4 snowmen and 3 ornaments of Santa Claus: $\$ 34$ 
B)  $\quad 3$ snowmen and 4 ornaments of Santa Claus: $\$ 34$ 
C)  4 snowmen and 2 ornaments of Santa Claus: $\$ 480$ 
D)  $\quad 2$ snowmen and 5 ornaments of Santa Claus: $\$ 46$ 
E)  $\quad 5$ snowmen and no ornaments of Santa Claus: $\$ 415$ 
A)  4 snowmen and 3 ornaments of Santa Claus: $\$ 34$ 
B)  $\quad 3$ snowmen and 4 ornaments of Santa Claus: $\$ 34$ 
C)  4 snowmen and 2 ornaments of Santa Claus: $\$ 480$ 
D)  $\quad 2$ snowmen and 5 ornaments of Santa Claus: $\$ 46$ 
E)  $\quad 5$ snowmen and no ornaments of Santa Claus: $\$ 415$

Question 3

Decompose the fraction into partial fractions. $$\frac { 7 x - 11 } { x ^ { 2 } + 2 x - 3 }$$

Accepted Answer

A)  $\quad \frac { 8 } { x + 3 } - \frac { 1 } { x - 1 }$ 
B)  $\quad \frac { 8 } { x + 3 } + \frac { 1 } { x - 2 }$ 
C)  $\quad \frac { 6 } { x - 3 } + \frac { 1 } { x + 1 }$ 
D)  $\quad \frac { 6 } { x - 3 } - \frac { 1 } { x + 1 }$ 
E)  none of these 
A)  $\quad \frac { 8 } { x + 3 } - \frac { 1 } { x - 1 }$ 
B)  $\quad \frac { 8 } { x + 3 } + \frac { 1 } { x - 2 }$ 
C)  $\quad \frac { 6 } { x - 3 } + \frac { 1 } { x + 1 }$ 
D)  $\quad \frac { 6 } { x - 3 } - \frac { 1 } { x + 1 }$ 
E)  none of these

Question 4

Solve the system by the addition method, if possible. If a solution exists, give the value of y. $$\left\{ \begin{array} { l } 
\frac { x - 10 } { 5 } + \frac { y + 7 } { 3 } = \frac { 8 } { 15 } \
\frac { x + 7 } { 3 } + \frac { y - 10 } { 7 } = \frac { 52 } { 21 }
\end{array} \right.$$

Accepted Answer

A)  10 
B)  6 
C)  $- 3$ 
D)  4 
E)  no solution 
A)  10 
B)  6 
C)  $- 3$ 
D)  4 
E)  no solution

Question 5

Minimize $P = 16 x + 2 y$ subject to the given constraints.
$\left\{\begin{aligned}
x & \geq 0 \
y & \geq 0 \
x+2 y & \geq 8 \
2 x+y & \geq 8
\end{aligned}\right.$

Accepted Answer

A)  $\quad P = 72$ at $( 4,4 )$ 
B)  $\quad P = 16$ at $( 0,8 )$ 
C)  $\quad P = 8$ at $( 0,2 )$ 
D)  $\quad P = - 32$ at $( - 2,0 )$ 
E)  none of these 
A)  $\quad P = 72$ at $( 4,4 )$ 
B)  $\quad P = 16$ at $( 0,8 )$ 
C)  $\quad P = 8$ at $( 0,2 )$ 
D)  $\quad P = - 32$ at $( - 2,0 )$ 
E)  none of these

Question 6

Use Cramer's rule to find the solution of the system, if possible. $$\left\{ \begin{array} { c } 
x - y - z = 1 \
x + y + z = 19 \
- x - y + z = - 11
\end{array} \right.$$

Accepted Answer

A)  $x = 10 , y = 5 , z = 4$ 
B)  $x = 5 , y = 10 , z = 4$ 
C)  $x = 4 , y = 5 , z = 10$ 
D)  The system is inconsistent. 
E)  The equations are dependent. 
A)  $x = 10 , y = 5 , z = 4$ 
B)  $x = 5 , y = 10 , z = 4$ 
C)  $x = 4 , y = 5 , z = 10$ 
D)  The system is inconsistent. 
E)  The equations are dependent.

Question 7

Minimize $P = 18 x + 4 y$ subject to the given constraints.
$\left\{\begin{array}{rll}
x & \geq & 0 \
y & \geq & 0 \
x+4 y & \geq & 9 \
4 x+y & \geq & 9
\end{array}\right.$

Accepted Answer

A)  $\quad P = 99$ at $( 4.5,4.5 )$ 
B)  $\quad P = 9$ at $( 0,4 )$ 
C)  $\quad P = - 72$ at $( - 4,0 )$ 
D)  $\quad P = 36$ at $( 0,9 )$ 
E)  none of these 
A)  $\quad P = 99$ at $( 4.5,4.5 )$ 
B)  $\quad P = 9$ at $( 0,4 )$ 
C)  $\quad P = - 72$ at $( - 4,0 )$ 
D)  $\quad P = 36$ at $( 0,9 )$ 
E)  none of these

Question 8

Decompose the fraction into partial fractions. $$\frac { 7 x ^ { 2 } + 6 x + 7 } { x ^ { 3 } + x }$$

Accepted Answer

A)  $\frac { 7 } { x } - \frac { 6 } { x ^ { 2 } + 1 }$ 
B)  $\frac { 6 } { x } - \frac { 7 } { x ^ { 2 } + 1 }$ 
C)  $\frac { 7 } { x } + \frac { 6 } { x ^ { 2 } + 1 }$ 
D)  $\frac { 6 } { x } + \frac { 7 } { x ^ { 2 } + 1 }$ 
E)  none of these 
A)  $\frac { 7 } { x } - \frac { 6 } { x ^ { 2 } + 1 }$ 
B)  $\frac { 6 } { x } - \frac { 7 } { x ^ { 2 } + 1 }$ 
C)  $\frac { 7 } { x } + \frac { 6 } { x ^ { 2 } + 1 }$ 
D)  $\frac { 6 } { x } + \frac { 7 } { x ^ { 2 } + 1 }$ 
E)  none of these

Question 9

Find the inverse of the matrix.
$$\left[ \begin{array} { c c } 
2 & 1 \
- 1 & 16
\end{array} \right]$$

Accepted Answer

A)  $\left[ \begin{array} { c c } \frac { 16 } { 33 } & - \frac { 1 } { 33 } \ - \frac { 1 } { 33 } & \frac { 2 } { 33 } \end{array} \right]$ 
B)  $\left[ \begin{array} { c c } \frac { 16 } { 33 } & \frac { 1 } { 33 } \ \frac { 1 } { 33 } & \frac { 2 } { 33 } \end{array} \right]$ 
C) 
$$\left[ \begin{array} { c c } 
\frac { 16 } { 33 } & - \frac { 1 } { 33 } \
\frac { 1 } { 33 } & - \frac { 2 } { 33 }
\end{array} \right]$$ 
D)  $\left[ \begin{array} { c c } - \frac { 16 } { 33 } & - \frac { 1 } { 33 } \ \frac { 1 } { 33 } & \frac { 2 } { 33 } \end{array} \right]$ 
E)  $\left[ \begin{array} { c c } \frac { 16 } { 33 } & - \frac { 1 } { 33 } \ \frac { 1 } { 33 } & \frac { 2 } { 33 } \end{array} \right]$ 
A)  $\left[ \begin{array} { c c } \frac { 16 } { 33 } & - \frac { 1 } { 33 } \ - \frac { 1 } { 33 } & \frac { 2 } { 33 } \end{array} \right]$ 
B)  $\left[ \begin{array} { c c } \frac { 16 } { 33 } & \frac { 1 } { 33 } \ \frac { 1 } { 33 } & \frac { 2 } { 33 } \end{array} \right]$ 
C) 
$$\left[ \begin{array} { c c } 
\frac { 16 } { 33 } & - \frac { 1 } { 33 } \
\frac { 1 } { 33 } & - \frac { 2 } { 33 }
\end{array} \right]$$ 
D)  $\left[ \begin{array} { c c } - \frac { 16 } { 33 } & - \frac { 1 } { 33 } \ \frac { 1 } { 33 } & \frac { 2 } { 33 } \end{array} \right]$ 
E)  $\left[ \begin{array} { c c } \frac { 16 } { 33 } & - \frac { 1 } { 33 } \ \frac { 1 } { 33 } & \frac { 2 } { 33 } \end{array} \right]$

Question 10

Solve the system by the addition method, if possible. If a solution exists, give the value of y. $\left\{ \begin{array} { l } 
\frac { x - 10 } { 5 } + \frac { y + 3 } { 3 } = - \frac { 37 } { 15 } \
\frac { x + 3 } { 3 } + \frac { y - 10 } { 7 } = - \frac { 17 } { 21 }
\end{array} \right.$

Accepted Answer

A)  $- 5$ 
B)  1 
C) -3 
D)  7 
E)  no solution 
A)  $- 5$ 
B)  1 
C) -3 
D)  7 
E)  no solution

Use a graphing calculator to approximate the solutions of the system. $\left\{ \begin{array} { c } 3.8 x + 3.9 y = 38.03 \\- 9 x + 4 y = 14.5\end{array} \right.$

Decompose the fraction into partial fractions. $\frac { 7 x - 11 } { x ^ { 2 } + 2 x - 3 }$

Solve the system by the addition method, if possible. If a solution exists, give the value of y. $\left\{ \begin{array} { l } \frac { x - 10 } { 5 } + \frac { y + 7 } { 3 } = \frac { 8 } { 15 } \\\frac { x + 7 } { 3 } + \frac { y - 10 } { 7 } = \frac { 52 } { 21 }\end{array} \right.$

Minimize $P = 16 x + 2 y$ subject to the given constraints. $\left\{\begin{aligned}x & \geq 0 \\y & \geq 0 \\x+2 y & \geq 8 \\2 x+y & \geq 8\end{aligned}\right.$

Use Cramer's rule to find the solution of the system, if possible. $\left\{ \begin{array} { c } x - y - z = 1 \\x + y + z = 19 \\- x - y + z = - 11\end{array} \right.$

Minimize $P = 18 x + 4 y$ subject to the given constraints. $\left\{\begin{array}{rll}x & \geq & 0 \\y & \geq & 0 \\x+4 y & \geq & 9 \\4 x+y & \geq & 9\end{array}\right.$

Decompose the fraction into partial fractions. $\frac { 7 x ^ { 2 } + 6 x + 7 } { x ^ { 3 } + x }$

Find the inverse of the matrix. $\left[ \begin{array} { c c } 2 & 1 \\- 1 & 16\end{array} \right]$

Solve the system by the addition method, if possible. If a solution exists, give the value of y. $\left\{ \begin{array} { l } \frac { x - 10 } { 5 } + \frac { y + 3 } { 3 } = - \frac { 37 } { 15 } \\\frac { x + 3 } { 3 } + \frac { y - 10 } { 7 } = - \frac { 17 } { 21 }\end{array} \right.$

A Review of Basic Algebra

Equations and Inequalities

The Rectangular Coordinate System and Graphs of Equations

Functions Functions and Function Notation

Exponential and Logarithmic Functions

Solving Polynomial Equations

Conic Sections and Quadratic Systems

Natural Number Functions and Probability

Filters

Exam 7: Linear Systems

Use a graphing calculator to approximate the solutions of the system. {3.8x+3.9y=38.03−9x+4y=14.5\left\{ \begin{array} { c } 3.8 x + 3.9 y = 38.03 \\- 9 x + 4 y = 14.5\end{array} \right.{3.8x+3.9y=38.03−9x+4y=14.5​

Decompose the fraction into partial fractions. 7x−11x2+2x−3\frac { 7 x - 11 } { x ^ { 2 } + 2 x - 3 }x2+2x−37x−11​

Minimize P=16x+2yP = 16 x + 2 yP=16x+2y subject to the given constraints. {x≥0y≥0x+2y≥82x+y≥8\left\{\begin{aligned}x & \geq 0 \\y & \geq 0 \\x+2 y & \geq 8 \\2 x+y & \geq 8\end{aligned}\right.⎩⎨⎧​xyx+2y2x+y​≥0≥0≥8≥8​

Use Cramer's rule to find the solution of the system, if possible. {x−y−z=1x+y+z=19−x−y+z=−11\left\{ \begin{array} { c } x - y - z = 1 \\x + y + z = 19 \\- x - y + z = - 11\end{array} \right.⎩⎨⎧​x−y−z=1x+y+z=19−x−y+z=−11​

Minimize P=18x+4yP = 18 x + 4 yP=18x+4y subject to the given constraints. {x≥0y≥0x+4y≥94x+y≥9\left\{\begin{array}{rll}x & \geq & 0 \\y & \geq & 0 \\x+4 y & \geq & 9 \\4 x+y & \geq & 9\end{array}\right.⎩⎨⎧​xyx+4y4x+y​≥≥≥≥​0099​

Decompose the fraction into partial fractions. 7x2+6x+7x3+x\frac { 7 x ^ { 2 } + 6 x + 7 } { x ^ { 3 } + x }x3+x7x2+6x+7​

Find the inverse of the matrix. [21−116]\left[ \begin{array} { c c } 2 & 1 \\- 1 & 16\end{array} \right][2−1​116​]