Question 1

Use Cramer s rule to solve the system of equations, if possible. $\left\{ \begin{array} { l } 
x + y = 8 \
x - y = 6
\end{array} \right.$

Accepted Answer

A)  (1,7) 
B)  (7,1) 
C)  (8,6) 
D)  dependent 
E)  inconsistent 
A)  (1,7) 
B)  (7,1) 
C)  (8,6) 
D)  dependent 
E)  inconsistent B

Question 2

Use Cramer s rule to solve the system of equations, if possible. $\left\{ \begin{array} { l } 
4 x + 3 y = 12 \
x - 3 = - \frac { 3 y } { 4 }
\end{array} \right.$

Accepted Answer

A)  (4,-3) 
B)  (-8,4) 
C)  (4,6) 
D)  dependent 
E)  inconsistent 
A)  (4,-3) 
B)  (-8,4) 
C)  (4,6) 
D)  dependent 
E)  inconsistent D

Question 3

Solve the system by any method, if possible. $\sqrt { - 2 } \sqrt { - 14 }$

Accepted Answer

A)  $7 \sqrt { 2 } i$ 
B)  $2 \sqrt { 7 } i$ 
C)  $- 2 \sqrt { 7 }$ 
D)  infinitely many solutions, dependent equations 
E)  no solution, inconsistent system 
A)  $7 \sqrt { 2 } i$ 
B)  $2 \sqrt { 7 } i$ 
C)  $- 2 \sqrt { 7 }$ 
D)  infinitely many solutions, dependent equations 
E)  no solution, inconsistent system B

Question 4

Use matrices to solve the system of equations. If the equations of the system are dependent, or if the system is inconsistent, so indicate. $\left\{ \begin{array} { l } 
2 x + 4 y = 2 \
9 x - 2 y = 29
\end{array} \right.$

Accepted Answer

The answer of Use matrices to solve the system of...

Question 5

The graph of the equation $7 x + 2 y + 6 z = 9$ is a flat surface called a __________.

Accepted Answer

The answer of The graph of the equation \(7 x...

Question 6

Solve the system. $\left\{ \begin{array} { l } 
4 x + 3 y = 5 - 2 z \
2 x = 3 y + 4 z - 4 \
8 x + 6 y + 4 z = 10
\end{array} \right.$

Accepted Answer

A)  $( 5,0,2 )$ 
B)  $( 5 , - 1 , - 2 )$ 
C)  $( 5,0 , - 2 )$ 
D)  The system is inconsistent. 
E)  The equations are dependent. 
A)  $( 5,0,2 )$ 
B)  $( 5 , - 1 , - 2 )$ 
C)  $( 5,0 , - 2 )$ 
D)  The system is inconsistent. 
E)  The equations are dependent.

Question 7

Find the equation of the parabola that passes through the points (4, 0), (3, 5), and (-3,-7).

Accepted Answer

A)  $y = x ^ { 2 } - 2 x + 2$ 
B)  $y = - x ^ { 2 } + 2 x + 8$ 
C)  $y = x ^ { 2 } + 2 x + 8$ 
D)  $y = - x ^ { 2 } - 2 x + 8$ 
A)  $y = x ^ { 2 } - 2 x + 2$ 
B)  $y = - x ^ { 2 } + 2 x + 8$ 
C)  $y = x ^ { 2 } + 2 x + 8$ 
D)  $y = - x ^ { 2 } - 2 x + 8$

Question 8

Solve the system by elimination if possible. $3 ^ { 3 x - 3 } = 729$

Accepted Answer

A)  (1, 6) 
B)  $\left\{ \frac { 7 } { 2 } \right\}$ 
C)  (6, 1) 
D)  infinitely many solutions, dependent equations 
E)  no solution, inconsistent system 
A)  (1, 6) 
B)  $\left\{ \frac { 7 } { 2 } \right\}$ 
C)  (6, 1) 
D)  infinitely many solutions, dependent equations 
E)  no solution, inconsistent system

Question 9

Evaluate the determinant. $\left| \begin{array} { r r r } 
- 1 & 5 & 1 \
- 5 & 1 & - 2 \
1 & 1 & 1
\end{array} \right|$

Accepted Answer

A)  10 
B)  -9 
C)  8 
D)  6 
E)  -5 
A)  10 
B)  -9 
C)  8 
D)  6 
E)  -5

Question 10

How many milliliters of a 5% acid solution and a 13% acid solution should be used to make 200 ml of an 8% acid solution? Choose the system that would solve the application. Let x = number of liters of 5% acid solution and y = number of liters of 13% acid solution.

Accepted Answer

A)  $\left\{ \begin{array} { l } 
x + y = 200 \
.05 x + .13 y = 16
\end{array} \right.$ 
B)  $\left\{ \begin{array} { l } 
x + y = 200 \
.05 x + .13 y = 200
\end{array} \right.$ 
C)  $\left\{ \begin{array} { l } 
x + 200 = y \
.05 x + .13 y = 16
\end{array} \right.$ 
D)  $\left\{ \begin{array} { l } 
x + y = 200 \
.05 x + .13 y = 190
\end{array} \right.$ 
A)  $\left\{ \begin{array} { l } 
x + y = 200 \
.05 x + .13 y = 16
\end{array} \right.$ 
B)  $\left\{ \begin{array} { l } 
x + y = 200 \
.05 x + .13 y = 200
\end{array} \right.$ 
C)  $\left\{ \begin{array} { l } 
x + 200 = y \
.05 x + .13 y = 16
\end{array} \right.$ 
D)  $\left\{ \begin{array} { l } 
x + y = 200 \
.05 x + .13 y = 190
\end{array} \right.$

Question 11

Solve the system. If a system is inconsistent or if the equations are dependent, so indicate. $\left\{ \begin{array} { l } 
r - s + t = 6 \
r + 2 s - t = - 1 \
r + s - 3 t = - 4
\end{array} \right.$

Accepted Answer

The answer of Solve the system. If a system is...

Question 12

Solve the following system of equations by elimination. $a + b i$

Accepted Answer

A)  $( 4 + 2 i ) ( 1 - 9 i )$ 
B)  (4, 6) 
C)  infinitely many solutions; dependent equations 
D)  no solution; inconsistent system 
A)  $( 4 + 2 i ) ( 1 - 9 i )$ 
B)  (4, 6) 
C)  infinitely many solutions; dependent equations 
D)  no solution; inconsistent system

Question 13

Use Cramer s rule to solve the system of equations, if possible. If the equations of the system are dependent, or if the system is inconsistent, so indicate. $\left\{ \begin{array} { l } 
x + y + 2 z = 12 \
x + 2 y + z = 11 \
2 x + y + z = 9
\end{array} \right.$

Accepted Answer

The answer of Use Cramer s rule to solve the...

Question 14

Use matrices to solve the system of equations. If the equations of the system are dependent, or if the system is inconsistent, so indicate. $\left\{ \begin{array} { l } 
3 x + y = 13 \
x + 3 y = - 1
\end{array} \right.$

Accepted Answer

The answer of Use matrices to solve the system of...

Question 15

Solve the system by any method, if possible. $\log _ { 4 } \frac { 4 x ^ { 9 } } { y }$

Accepted Answer

A)  $1 + \log _ { 4 } 9 x - \log _ { 4 } y$ 
B)  $1 + 9 \log _ { 4 } x - \log _ { 4 } y$ 
C)  $\log _ { 4 } 36 + \log _ { 4 } x - \log _ { 4 } y$ 
D)  infinitely many solutions, dependent equations 
E)  no solution, inconsistent system 
A)  $1 + \log _ { 4 } 9 x - \log _ { 4 } y$ 
B)  $1 + 9 \log _ { 4 } x - \log _ { 4 } y$ 
C)  $\log _ { 4 } 36 + \log _ { 4 } x - \log _ { 4 } y$ 
D)  infinitely many solutions, dependent equations 
E)  no solution, inconsistent system

Question 16

Solve the system by substitution, if possible. $5 ^ { x } = 9$

Accepted Answer

A)  $- 0.5579$ 
B)  $- 1.7925$ 
C)  $v ^ { - 3 }$ 
D)  infinitely many solutions, dependent equations 
E)  no solution, inconsistent system 
A)  $- 0.5579$ 
B)  $- 1.7925$ 
C)  $v ^ { - 3 }$ 
D)  infinitely many solutions, dependent equations 
E)  no solution, inconsistent system

Question 17

Find a cubic equation of the form $y = a x ^ { 3 } + c x + d$ passing through the points $( - 2 , - 16 ) , ( 0,4 ) , ( 1,5 ) \text {, and } ( 3,79 )$ .

Accepted Answer

The answer of Find a cubic equation of the form...

Question 18

Solve the system $\left\{ \begin{array} { l } 
9 x - y = 7 \
8 x + 9 y = - 9
\end{array} \right.$ by Cramer s rule. Write the determinant $D _ { x }$ .

Accepted Answer

A)  $\mid \begin{array} { c c } 
9 & - 1 \
8 & 9
\end{array}$ 
B)  $\left| \begin{array} { c c } 
7 & - 1 \
- 9 & 9
\end{array} \right|$ 
C)  $\begin{array} { c c } 
9 & 7 \
8 & - 9
\end{array}$ 
D)  $\left| \begin{array} { c c } 
- 7 & - 1 \
9 & 9
\end{array} \right|$ 
A)  $\mid \begin{array} { c c } 
9 & - 1 \
8 & 9
\end{array}$ 
B)  $\left| \begin{array} { c c } 
7 & - 1 \
- 9 & 9
\end{array} \right|$ 
C)  $\begin{array} { c c } 
9 & 7 \
8 & - 9
\end{array}$ 
D)  $\left| \begin{array} { c c } 
- 7 & - 1 \
9 & 9
\end{array} \right|$

Question 19

Explain what $5 R _ { 1 } + R _ { 2 }$ means.

Accepted Answer

Add row 2

Question 20

Evaluate the determinant. $$\left| \begin{array} { c c c } 
7 & 1 & - 6 \
2 & 3 & 2 \
- 5 & 2 & 7
\end{array} \right|$$

Accepted Answer

A)  -19 
B)  -52 
C)  48 
D)  none of these 
A)  -19 
B)  -52 
C)  48 
D)  none of these

Use Cramer s rule to solve the system of equations, if possible. $\left\{ \begin{array} { l } x + y = 8 \\x - y = 6\end{array} \right.$

Use Cramer s rule to solve the system of equations, if possible. $\left\{ \begin{array} { l } 4 x + 3 y = 12 \\x - 3 = - \frac { 3 y } { 4 }\end{array} \right.$

Solve the system by any method, if possible. $\sqrt { - 2 } \sqrt { - 14 }$

Use matrices to solve the system of equations. If the equations of the system are dependent, or if the system is inconsistent, so indicate. $\left\{ \begin{array} { l } 2 x + 4 y = 2 \\9 x - 2 y = 29\end{array} \right.$

The graph of the equation $7 x + 2 y + 6 z = 9$ is a flat surface called a __________.

Solve the system. $\left\{ \begin{array} { l } 4 x + 3 y = 5 - 2 z \\2 x = 3 y + 4 z - 4 \\8 x + 6 y + 4 z = 10\end{array} \right.$

Find the equation of the parabola that passes through the points (4, 0), (3, 5), and (-3,-7).

Solve the system by elimination if possible. $3 ^ { 3 x - 3 } = 729$

Evaluate the determinant. $\left| \begin{array} { r r r } - 1 & 5 & 1 \\- 5 & 1 & - 2 \\1 & 1 & 1\end{array} \right|$

How many milliliters of a 5% acid solution and a 13% acid solution should be used to make 200 ml of an 8% acid solution? Choose the system that would solve the application. Let x = number of liters of 5% acid solution and y = number of liters of 13% acid solution.

Solve the system. If a system is inconsistent or if the equations are dependent, so indicate. $\left\{ \begin{array} { l } r - s + t = 6 \\r + 2 s - t = - 1 \\r + s - 3 t = - 4\end{array} \right.$

Solve the following system of equations by elimination. $a + b i$

Use Cramer s rule to solve the system of equations, if possible. If the equations of the system are dependent, or if the system is inconsistent, so indicate. $\left\{ \begin{array} { l } x + y + 2 z = 12 \\x + 2 y + z = 11 \\2 x + y + z = 9\end{array} \right.$

Use matrices to solve the system of equations. If the equations of the system are dependent, or if the system is inconsistent, so indicate. $\left\{ \begin{array} { l } 3 x + y = 13 \\x + 3 y = - 1\end{array} \right.$

Solve the system by any method, if possible. $\log _ { 4 } \frac { 4 x ^ { 9 } } { y }$

Solve the system by substitution, if possible. $5 ^ { x } = 9$

Find a cubic equation of the form $y = a x ^ { 3 } + c x + d$ passing through the points $( - 2 , - 16 ) , ( 0,4 ) , ( 1,5 ) \text {, and } ( 3,79 )$ .

Solve the system $\left\{ \begin{array} { l } 9 x - y = 7 \\8 x + 9 y = - 9\end{array} \right.$ by Cramer s rule. Write the determinant $D _ { x }$ .

Explain what $5 R _ { 1 } + R _ { 2 }$ means.

Evaluate the determinant. $\left| \begin{array} { c c c } 7 & 1 & - 6 \\2 & 3 & 2 \\- 5 & 2 & 7\end{array} \right|$

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 Cramer s rule to solve the system of equations, if possible. {x+y=8x−y=6\left\{ \begin{array} { l } x + y = 8 \\x - y = 6\end{array} \right.{x+y=8x−y=6​

Use Cramer s rule to solve the system of equations, if possible. {4x+3y=12x−3=−3y4\left\{ \begin{array} { l } 4 x + 3 y = 12 \\x - 3 = - \frac { 3 y } { 4 }\end{array} \right.{4x+3y=12x−3=−43y​​

Solve the system by any method, if possible. −2−14\sqrt { - 2 } \sqrt { - 14 }−2​−14​

Use matrices to solve the system of equations. If the equations of the system are dependent, or if the system is inconsistent, so indicate. {2x+4y=29x−2y=29\left\{ \begin{array} { l } 2 x + 4 y = 2 \\9 x - 2 y = 29\end{array} \right.{2x+4y=29x−2y=29​

The graph of the equation 7x+2y+6z=97 x + 2 y + 6 z = 97x+2y+6z=9 is a flat surface called a __________.

Solve the system. {4x+3y=5−2z2x=3y+4z−48x+6y+4z=10\left\{ \begin{array} { l } 4 x + 3 y = 5 - 2 z \\2 x = 3 y + 4 z - 4 \\8 x + 6 y + 4 z = 10\end{array} \right.⎩⎨⎧​4x+3y=5−2z2x=3y+4z−48x+6y+4z=10​

Find the equation of the parabola that passes through the points (4, 0), (3, 5), and (-3,-7).

Solve the system by elimination if possible. 33x−3=7293 ^ { 3 x - 3 } = 72933x−3=729

Evaluate the determinant. ∣−151−51−2111∣\left| \begin{array} { r r r } - 1 & 5 & 1 \\- 5 & 1 & - 2 \\1 & 1 & 1\end{array} \right|​−1−51​511​1−21​​

How many milliliters of a 5% acid solution and a 13% acid solution should be used to make 200 ml of an 8% acid solution? Choose the system that would solve the application. Let x = number of liters of 5% acid solution and y = number of liters of 13% acid solution.

Solve the system. If a system is inconsistent or if the equations are dependent, so indicate. {r−s+t=6r+2s−t=−1r+s−3t=−4\left\{ \begin{array} { l } r - s + t = 6 \\r + 2 s - t = - 1 \\r + s - 3 t = - 4\end{array} \right.⎩⎨⎧​r−s+t=6r+2s−t=−1r+s−3t=−4​

Solve the following system of equations by elimination. a+bia + b ia+bi

Use matrices to solve the system of equations. If the equations of the system are dependent, or if the system is inconsistent, so indicate. {3x+y=13x+3y=−1\left\{ \begin{array} { l } 3 x + y = 13 \\x + 3 y = - 1\end{array} \right.{3x+y=13x+3y=−1​

Solve the system by any method, if possible. log⁡44x9y\log _ { 4 } \frac { 4 x ^ { 9 } } { y }log4​y4x9​

Solve the system by substitution, if possible. 5x=95 ^ { x } = 95x=9

Find a cubic equation of the form y=ax3+cx+dy = a x ^ { 3 } + c x + dy=ax3+cx+d passing through the points (−2,−16),(0,4),(1,5), and (3,79)( - 2 , - 16 ) , ( 0,4 ) , ( 1,5 ) \text {, and } ( 3,79 )(−2,−16),(0,4),(1,5), and (3,79) .

Solve the system {9x−y=78x+9y=−9\left\{ \begin{array} { l } 9 x - y = 7 \\8 x + 9 y = - 9\end{array} \right.{9x−y=78x+9y=−9​ by Cramer s rule. Write the determinant DxD _ { x }Dx​ .

Explain what 5R1+R25 R _ { 1 } + R _ { 2 }5R1​+R2​ means.

Evaluate the determinant. ∣71−6232−527∣\left| \begin{array} { c c c } 7 & 1 & - 6 \\2 & 3 & 2 \\- 5 & 2 & 7\end{array} \right|​72−5​132​−627​​

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 Cramer s rule to solve the system of equations, if possible. $\left\{ \begin{array} { l } x + y = 8 \\x - y = 6\end{array} \right.$

Use Cramer s rule to solve the system of equations, if possible. $\left\{ \begin{array} { l } 4 x + 3 y = 12 \\x - 3 = - \frac { 3 y } { 4 }\end{array} \right.$

Solve the system by any method, if possible. $\sqrt { - 2 } \sqrt { - 14 }$

Use matrices to solve the system of equations. If the equations of the system are dependent, or if the system is inconsistent, so indicate. $\left\{ \begin{array} { l } 2 x + 4 y = 2 \\9 x - 2 y = 29\end{array} \right.$

The graph of the equation $7 x + 2 y + 6 z = 9$ is a flat surface called a __________.

Solve the system. $\left\{ \begin{array} { l } 4 x + 3 y = 5 - 2 z \\2 x = 3 y + 4 z - 4 \\8 x + 6 y + 4 z = 10\end{array} \right.$

Solve the system by elimination if possible. $3 ^ { 3 x - 3 } = 729$

Evaluate the determinant. $\left| \begin{array} { r r r } - 1 & 5 & 1 \\- 5 & 1 & - 2 \\1 & 1 & 1\end{array} \right|$

Solve the system. If a system is inconsistent or if the equations are dependent, so indicate. $\left\{ \begin{array} { l } r - s + t = 6 \\r + 2 s - t = - 1 \\r + s - 3 t = - 4\end{array} \right.$

Solve the following system of equations by elimination. $a + b i$

Use matrices to solve the system of equations. If the equations of the system are dependent, or if the system is inconsistent, so indicate. $\left\{ \begin{array} { l } 3 x + y = 13 \\x + 3 y = - 1\end{array} \right.$

Solve the system by any method, if possible. $\log _ { 4 } \frac { 4 x ^ { 9 } } { y }$

Solve the system by substitution, if possible. $5 ^ { x } = 9$

Find a cubic equation of the form $y = a x ^ { 3 } + c x + d$ passing through the points $( - 2 , - 16 ) , ( 0,4 ) , ( 1,5 ) \text {, and } ( 3,79 )$ .

Solve the system $\left\{ \begin{array} { l } 9 x - y = 7 \\8 x + 9 y = - 9\end{array} \right.$ by Cramer s rule. Write the determinant $D _ { x }$ .

Explain what $5 R _ { 1 } + R _ { 2 }$ means.

Evaluate the determinant. $\left| \begin{array} { c c c } 7 & 1 & - 6 \\2 & 3 & 2 \\- 5 & 2 & 7\end{array} \right|$