Question 1

Solve for the x -coordinate of the solution of the following system. $\left\{ \begin{array} { l } 
x + 2 y - z = 0 \
x - 4 y + z = - 8 \
x + 4 y - 2 z = 5
\end{array} \right.$

Accepted Answer

A)  x=-5 
B)  x=5 
C)  x=4 
D)  x=-4 
A)  x=-5 
B)  x=5 
C)  x=4 
D)  x=-4

Question 2

Solve: $\left\{ \begin{array} { l } 
5 a + 5 b - 3 c + 9 d = - 6 \
3 a - 9 b - 9 c - 2 d = - 11 \
6 a - 3 b + 6 c + 9 d = - 9 \
a - b + c + d = - 2
\end{array} \right.$

Accepted Answer

The answer of Solve: \(\left\{ \begin{array} { l } 
5...

Question 3

Write the determinant $D_{y}$ for the system $\left\{ \begin{array} { l } 
8 x + 3 y + 5 z = 2 \
4 x - 3 y - 8 z = - 5 \
9 x + 6 y + 8 z = 5
\end{array} \right.$

Accepted Answer

A)  $\left| \begin{array} { c c c } 
8 & 3 & 5 \
4 & - 3 & - 8 \
9 & 6 & 8
\end{array} \right|$ 
B)  $\left| \begin{array} { c c c } 
2 & 3 & 5 \
- 5 & - 3 & - 8 \
5 & 6 & 8
\end{array} \right|$ 
C)  $\left| \begin{array} { c c c } 
8 & 3 & 2 \
4 & - 3 & - 5 \
9 & 6 & 5
\end{array} \right|$ 
D)  $\left| \begin{array} { c c c } 
8 & 2 & 5 \
4 & - 5 & - 8 \
9 & 5 & 8
\end{array} \right|$ 
A)  $\left| \begin{array} { c c c } 
8 & 3 & 5 \
4 & - 3 & - 8 \
9 & 6 & 8
\end{array} \right|$ 
B)  $\left| \begin{array} { c c c } 
2 & 3 & 5 \
- 5 & - 3 & - 8 \
5 & 6 & 8
\end{array} \right|$ 
C)  $\left| \begin{array} { c c c } 
8 & 3 & 2 \
4 & - 3 & - 5 \
9 & 6 & 5
\end{array} \right|$ 
D)  $\left| \begin{array} { c c c } 
8 & 2 & 5 \
4 & - 5 & - 8 \
9 & 5 & 8
\end{array} \right|$

Question 4

A matrix that represents the equations of a system is called a(n) __________ matrix.

Accepted Answer

A)  identity 
B)  diagonal 
C)  dependent 
D)  inconsistent 
E)  augmented 
A)  identity 
B)  diagonal 
C)  dependent 
D)  inconsistent 
E)  augmented

Question 5

A clothing manufacturer makes coats, shirts, and slacks. The time required for cutting, sewing, and packaging each item is shown in the table. How many of each should be made to use all available labor hours?
 Coats Shirts Slacks Time available Cutting 20 min 15 min 10 min 120 hr Sewing 60 min 30 min 24 min 294 hr Packaging 5 min 12 min 6 min 67 hr __________ coats, __________ shirts, __________ slacks

Accepted Answer

The answer of A clothing manufacturer makes coats, shirts, and...

Question 6

Solve the system. If a system is inconsistent or if the equations are dependent, so indicate. $\left\{ \begin{array} { l } 
x + \frac { 1 } { 2 } y + z = 8 \
\frac { 1 } { 2 } x - y + \frac { 1 } { 2 } z = - 1 \
x + \frac { 1 } { 2 } y - \frac { 1 } { 2 } z = 2
\end{array} \right.$

Accepted Answer

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

Question 7

Solve $\left\{ \begin{array} { l } 
x + y = 1 \
x - y = 3
\end{array} \right.$

Accepted Answer

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

Question 8

A(n) __________ is a four-sided figure with two pairs of parallel sides.

Accepted Answer

The answer of A(n) __________ is a four-sided figure with...

Question 9

Evaluate the determinant. $\left| \begin{array} { r r } 
- 8 & 7 \
4 & - 2
\end{array} \right|$

Accepted Answer

The answer of Evaluate the determinant. \(\left| \begin{array} { r...

Question 10

Use matrices to solve the system of equations. If the equations of the system are dependent, or if the system is inconsistent, so indicate. $\left\{ \begin{array} { r } 
6 x + y - z = 1 \
x + 2 y + z = 5 \
5 y - z = 9
\end{array} \right.$

Accepted Answer

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

Question 11

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

Accepted Answer

The answer of Solve the system by elimination if possible....

Question 12

Evaluate the determinant. $\left| \begin{array} { r r r } 
1 & - 2 & 3 \
- 2 & 1 & 1 \
- 3 & - 2 & 1
\end{array} \right|$

Accepted Answer

A)  22 
B)  24 
C)  27 
D)  23 
E)  26 
A)  22 
B)  24 
C)  27 
D)  23 
E)  26

Question 13

Which of the following ordered triples is a solution of the system $\left\{ \begin{array} { l } 
3 x - 3 y + z = - 2 \
x - 5 y + 4 z = 7 \
3 x - 6 y - z = - 1
\end{array} \right.$

Accepted Answer

A)  (- 2, -1,-1) 
B)  (-2, 1, 13) 
C)  (- 2,-29,-1) 
D)  (- 2,-1, 1) 
A)  (- 2, -1,-1) 
B)  (-2, 1, 13) 
C)  (- 2,-29,-1) 
D)  (- 2,-1, 1)

Question 14

How many pounds of each candy shown in the illustration must be mixed to obtain 76 pounds of candy that would be worth $4 per pound?

Accepted Answer

A)  Gummy Bears: 57 lb; Jelly Beans: 20 lb 
B)  Gummy Bears: 58 lb; Jelly Beans: 20 lb 
C)  Gummy Bears: 55 lb; Jelly Beans: 19 lb 
D)  Gummy Bears: 58 lb; Jelly Beans: 19 lb 
E)  Gummy Bears: 57 lb; Jelly Beans: 19 lb 
A)  Gummy Bears: 57 lb; Jelly Beans: 20 lb 
B)  Gummy Bears: 58 lb; Jelly Beans: 20 lb 
C)  Gummy Bears: 55 lb; Jelly Beans: 19 lb 
D)  Gummy Bears: 58 lb; Jelly Beans: 19 lb 
E)  Gummy Bears: 57 lb; Jelly Beans: 19 lb

Question 15

Solve the following system of equations by graphing, if possible. Then write the solution as an ordered pair. If a system is inconsistent or if the equations are dependent, so indicate. $\left\{ \begin{array} { r } 
2 x + 3 y = 9 \
x = 3
\end{array} \right.$

Accepted Answer

A)  (1,3) 
B)  (3,1) 
C)  inconsistent 
D)  dependent 
A)  (1,3) 
B)  (3,1) 
C)  inconsistent 
D)  dependent

Question 16

Use matrices to find the y -coordinate of the solution of the following system. $\left\{ \begin{array} { l } 
x - 2 y = 26 \
3 x - y = 33
\end{array} \right.$

Accepted Answer

A)  y=-9 
B)  y=9 
C)  y=8 
D)  y=-8 
A)  y=-9 
B)  y=9 
C)  y=8 
D)  y=-8

Question 17

__________ rule uses determinants to solve systems of linear equations.

Accepted Answer

The answer of __________ rule uses determinants to solve systems...

Question 18

Elimination will be used to solve the system $a + b i$ . Which of the following equations is equivalent to equation 1 and can be added to equation 2 to eliminate y ?

Accepted Answer

A)  -24 x + 4 y = 28 
B)  24 x + 4 y = $\frac { 65 } { 8 - i }$ 7 
C)  24 x + 4 y = $4 - 7 i$ 28 
D)  none of these 
A)  -24 x + 4 y = 28 
B)  24 x + 4 y = $\frac { 65 } { 8 - i }$ 7 
C)  24 x + 4 y = $4 - 7 i$ 28 
D)  none of these

Question 19

Solve the system by graphing. $\left\{ \begin{array} { l } 
4 x = 4 - 3 y \
4 x + 3 y = 7
\end{array} \right.$

Accepted Answer

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

Question 20

For the augmented matrix, give the system of equations it represents. $\left[ \begin{array} { c c c | c } 
2 & - 2 & 8 & 1 \
3 & 1 & 1 & 0 \
2 & - 4 & 3 & - 7
\end{array} \right]$

Accepted Answer

A)  $\left\{ \begin{aligned}
- 2 x + 2 y = & 1 \
3 x - y = & 0 \
2 x + 4 y = & - 7
\end{aligned} \right.$ 
B)  $\left\{ \begin{array} { l } 
2 x - 2 y + 8 z = 1 \
3 x + y + z = 0 \
2 x - 4 y + 3 z = - 7
\end{array} \right.$ 
C)  $\left\{ \begin{array} { l } 
2 x - 2 y + 8 z = 0 \
3 x + y + z = 0 \
2 x - 4 y + 3 z = 0
\end{array} \right.$ 
D)  $\left\{ \begin{array} { r } 
- 2 x + 2 y = 0 \
3 x - y = 0 \
2 x + 4 y = 0
\end{array} \right.$ 
E)  $\left\{ \begin{array} { l } 
2 x - 2 y = 0 \
3 x + y = 0 \
2 x - 4 y = 0
\end{array} \right.$ 
A)  $\left\{ \begin{aligned}
- 2 x + 2 y = & 1 \
3 x - y = & 0 \
2 x + 4 y = & - 7
\end{aligned} \right.$ 
B)  $\left\{ \begin{array} { l } 
2 x - 2 y + 8 z = 1 \
3 x + y + z = 0 \
2 x - 4 y + 3 z = - 7
\end{array} \right.$ 
C)  $\left\{ \begin{array} { l } 
2 x - 2 y + 8 z = 0 \
3 x + y + z = 0 \
2 x - 4 y + 3 z = 0
\end{array} \right.$ 
D)  $\left\{ \begin{array} { r } 
- 2 x + 2 y = 0 \
3 x - y = 0 \
2 x + 4 y = 0
\end{array} \right.$ 
E)  $\left\{ \begin{array} { l } 
2 x - 2 y = 0 \
3 x + y = 0 \
2 x - 4 y = 0
\end{array} \right.$

Solve for the x -coordinate of the solution of the following system. $\left\{ \begin{array} { l } x + 2 y - z = 0 \\x - 4 y + z = - 8 \\x + 4 y - 2 z = 5\end{array} \right.$

Solve: $\left\{ \begin{array} { l } 5 a + 5 b - 3 c + 9 d = - 6 \\3 a - 9 b - 9 c - 2 d = - 11 \\6 a - 3 b + 6 c + 9 d = - 9 \\a - b + c + d = - 2\end{array} \right.$

Write the determinant $D_{y}$ for the system $\left\{ \begin{array} { l } 8 x + 3 y + 5 z = 2 \\4 x - 3 y - 8 z = - 5 \\9 x + 6 y + 8 z = 5\end{array} \right.$

A matrix that represents the equations of a system is called a(n) __________ matrix.

Solve the system. If a system is inconsistent or if the equations are dependent, so indicate. $\left\{ \begin{array} { l } x + \frac { 1 } { 2 } y + z = 8 \\\frac { 1 } { 2 } x - y + \frac { 1 } { 2 } z = - 1 \\x + \frac { 1 } { 2 } y - \frac { 1 } { 2 } z = 2\end{array} \right.$

Solve $\left\{ \begin{array} { l } x + y = 1 \\x - y = 3\end{array} \right.$

A(n) __________ is a four-sided figure with two pairs of parallel sides.

Evaluate the determinant. $\left| \begin{array} { r r } - 8 & 7 \\4 & - 2\end{array} \right|$

Use matrices to solve the system of equations. If the equations of the system are dependent, or if the system is inconsistent, so indicate. $\left\{ \begin{array} { r } 6 x + y - z = 1 \\x + 2 y + z = 5 \\5 y - z = 9\end{array} \right.$

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

Evaluate the determinant. $\left| \begin{array} { r r r } 1 & - 2 & 3 \\- 2 & 1 & 1 \\- 3 & - 2 & 1\end{array} \right|$

Which of the following ordered triples is a solution of the system $\left\{ \begin{array} { l } 3 x - 3 y + z = - 2 \\x - 5 y + 4 z = 7 \\3 x - 6 y - z = - 1\end{array} \right.$

How many pounds of each candy shown in the illustration must be mixed to obtain 76 pounds of candy that would be worth $4 per pound?

Use matrices to find the y -coordinate of the solution of the following system. $\left\{ \begin{array} { l } x - 2 y = 26 \\3 x - y = 33\end{array} \right.$

__________ rule uses determinants to solve systems of linear equations.

Elimination will be used to solve the system $a + b i$ . Which of the following equations is equivalent to equation 1 and can be added to equation 2 to eliminate y ?

Solve the system by graphing. $\left\{ \begin{array} { l } 4 x = 4 - 3 y \\4 x + 3 y = 7\end{array} \right.$

For the augmented matrix, give the system of equations it represents. $\left[ \begin{array} { c c c | c } 2 & - 2 & 8 & 1 \\3 & 1 & 1 & 0 \\2 & - 4 & 3 & - 7\end{array} \right]$

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

Solve for the x -coordinate of the solution of the following system. {x+2y−z=0x−4y+z=−8x+4y−2z=5\left\{ \begin{array} { l } x + 2 y - z = 0 \\x - 4 y + z = - 8 \\x + 4 y - 2 z = 5\end{array} \right.⎩⎨⎧​x+2y−z=0x−4y+z=−8x+4y−2z=5​

Write the determinant DyD_{y}Dy​ for the system {8x+3y+5z=24x−3y−8z=−59x+6y+8z=5\left\{ \begin{array} { l } 8 x + 3 y + 5 z = 2 \\4 x - 3 y - 8 z = - 5 \\9 x + 6 y + 8 z = 5\end{array} \right.⎩⎨⎧​8x+3y+5z=24x−3y−8z=−59x+6y+8z=5​

A matrix that represents the equations of a system is called a(n) __________ matrix.

Solve {x+y=1x−y=3\left\{ \begin{array} { l } x + y = 1 \\x - y = 3\end{array} \right.{x+y=1x−y=3​

A(n) __________ is a four-sided figure with two pairs of parallel sides.

Evaluate the determinant. ∣−874−2∣\left| \begin{array} { r r } - 8 & 7 \\4 & - 2\end{array} \right|​−84​7−2​​

Solve the system by elimination if possible. If the equations of the system are dependent, or if the system is inconsistent, so indicate. a+bia + b ia+bi

Evaluate the determinant. ∣1−23−211−3−21∣\left| \begin{array} { r r r } 1 & - 2 & 3 \\- 2 & 1 & 1 \\- 3 & - 2 & 1\end{array} \right|​1−2−3​−21−2​311​​

Which of the following ordered triples is a solution of the system {3x−3y+z=−2x−5y+4z=73x−6y−z=−1\left\{ \begin{array} { l } 3 x - 3 y + z = - 2 \\x - 5 y + 4 z = 7 \\3 x - 6 y - z = - 1\end{array} \right.⎩⎨⎧​3x−3y+z=−2x−5y+4z=73x−6y−z=−1​

How many pounds of each candy shown in the illustration must be mixed to obtain 76 pounds of candy that would be worth $4 per pound?

Solve the following system of equations by graphing, if possible. Then write the solution as an ordered pair. If a system is inconsistent or if the equations are dependent, so indicate. {2x+3y=9x=3\left\{ \begin{array} { r } 2 x + 3 y = 9 \\x = 3\end{array} \right.{2x+3y=9x=3​

Use matrices to find the y -coordinate of the solution of the following system. {x−2y=263x−y=33\left\{ \begin{array} { l } x - 2 y = 26 \\3 x - y = 33\end{array} \right.{x−2y=263x−y=33​

__________ rule uses determinants to solve systems of linear equations.

Elimination will be used to solve the system a+bia + b ia+bi . Which of the following equations is equivalent to equation 1 and can be added to equation 2 to eliminate y ?

Solve the system by graphing. {4x=4−3y4x+3y=7\left\{ \begin{array} { l } 4 x = 4 - 3 y \\4 x + 3 y = 7\end{array} \right.{4x=4−3y4x+3y=7​

For the augmented matrix, give the system of equations it represents. [2−28131102−43−7]\left[ \begin{array} { c c c | c } 2 & - 2 & 8 & 1 \\3 & 1 & 1 & 0 \\2 & - 4 & 3 & - 7\end{array} \right]​232​−21−4​813​10−7​​

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

Solve for the x -coordinate of the solution of the following system. $\left\{ \begin{array} { l } x + 2 y - z = 0 \\x - 4 y + z = - 8 \\x + 4 y - 2 z = 5\end{array} \right.$

Write the determinant $D_{y}$ for the system $\left\{ \begin{array} { l } 8 x + 3 y + 5 z = 2 \\4 x - 3 y - 8 z = - 5 \\9 x + 6 y + 8 z = 5\end{array} \right.$

Solve $\left\{ \begin{array} { l } x + y = 1 \\x - y = 3\end{array} \right.$

Evaluate the determinant. $\left| \begin{array} { r r } - 8 & 7 \\4 & - 2\end{array} \right|$

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

Evaluate the determinant. $\left| \begin{array} { r r r } 1 & - 2 & 3 \\- 2 & 1 & 1 \\- 3 & - 2 & 1\end{array} \right|$

Which of the following ordered triples is a solution of the system $\left\{ \begin{array} { l } 3 x - 3 y + z = - 2 \\x - 5 y + 4 z = 7 \\3 x - 6 y - z = - 1\end{array} \right.$

Use matrices to find the y -coordinate of the solution of the following system. $\left\{ \begin{array} { l } x - 2 y = 26 \\3 x - y = 33\end{array} \right.$

Elimination will be used to solve the system $a + b i$ . Which of the following equations is equivalent to equation 1 and can be added to equation 2 to eliminate y ?

Solve the system by graphing. $\left\{ \begin{array} { l } 4 x = 4 - 3 y \\4 x + 3 y = 7\end{array} \right.$

For the augmented matrix, give the system of equations it represents. $\left[ \begin{array} { c c c | c } 2 & - 2 & 8 & 1 \\3 & 1 & 1 & 0 \\2 & - 4 & 3 & - 7\end{array} \right]$