Question 1

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

Accepted Answer

The answer of Solve the system by any method, if...

Question 2

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

Accepted Answer

The answer of Solve the system by any method, if...

Question 3

Suppose a hammer can be manufactured in two different ways. The number of hammers that will cost equal amounts to produce either way is called the ________ point.

Accepted Answer

The answer of Suppose a hammer can be manufactured in...

Question 4

Refer to the illustration. 
 
 Decide whether a true or a false statement would be obtained when the coordinates of Point A  are substituted into the equation for line $l _ { 1 }$  . __________ Point B  are substituted into the equation for line $l _ { 1 }$ . __________ Point C are substituted into the equation for line $l _ { 1 }$ . __________ Point C are substituted into the equation for line $l _ { 2 }$ .__________

Accepted Answer

true; fals

Question 5

Which of the following is a 2×3 matrix?

Accepted Answer

A)  $\left[ \begin{array} { l l } 
2 & 3 \
3 & 0 \
9 & 5
\end{array} \right]$ 
B)  $\left[ \begin{array} { c c c c } 
2 & - 9 & 0 & 5 \
2 & 4 & - 4 & 3
\end{array} \right]$ 
C)  $\left[ \begin{array} { l l l } 
2 & 4 & 1 \
4 & 5 & 2
\end{array} \right]$ 
D)  $\left[ \begin{array} { l } 
5 \
6 \
4
\end{array} \right]$ 
A)  $\left[ \begin{array} { l l } 
2 & 3 \
3 & 0 \
9 & 5
\end{array} \right]$ 
B)  $\left[ \begin{array} { c c c c } 
2 & - 9 & 0 & 5 \
2 & 4 & - 4 & 3
\end{array} \right]$ 
C)  $\left[ \begin{array} { l l l } 
2 & 4 & 1 \
4 & 5 & 2
\end{array} \right]$ 
D)  $\left[ \begin{array} { l } 
5 \
6 \
4
\end{array} \right]$

Question 6

When three planes coincide, the equations of the system are ___________, and there are infinitely many solutions.

Accepted Answer

The answer of When three planes coincide, the equations of...

Question 7

Each number in a matrix is called a(n) __________ or entry of the matrix.

Accepted Answer

A)  element 
B)  row 
C)  diagonal 
D)  column 
E)  equation 
A)  element 
B)  row 
C)  diagonal 
D)  column 
E)  equation

Question 8

Use Cramer s rule to solve the system of equations, if possible. $\left\{ \begin{array} { l } 
2 x + y + z = 6 \
x - 2 y + 3 z = 8 \
x + y - 4 z = - 2
\end{array} \right.$

Accepted Answer

A)  $( 1 , - 1,3 )$ 
B)  $( 3 , - 1,1 )$ 
C)  $( 1 , - 3,1 )$ 
D)  dependent 
E)  inconsistent 
A)  $( 1 , - 1,3 )$ 
B)  $( 3 , - 1,1 )$ 
C)  $( 1 , - 3,1 )$ 
D)  dependent 
E)  inconsistent

Question 9

Find the y -coordinate of the solution of the system $\left\{ \begin{array} { l } 
x - y - 2 z = 15 \
3 x + 2 y - z = 20 \
x - y + z = 9
\end{array} \right.$

Accepted Answer

A)  y=3 
B)  y=-3 
C)  y=-8 
D)  y=-2 
A)  y=3 
B)  y=-3 
C)  y=-8 
D)  y=-2

Question 10

Refer to the illustration. 
 
How many ordered pairs satisfy the equation $3 x + y = 3$ ?
 __________ 
Complete the pairs, if they are known to satisfy the equation $3 x + y = 3$ . 
(-1,  ________  ),(0, ________),   (________, 0)

How many ordered pairs satisfy the equation $\frac { 1 } { 2 } x - y = - 3$ ?
 __________ 
Complete the pairs, if they are known to satisfy the equation $\frac { 1 } { 2 } x - y = - 3$ . 
(-2,  ________  ),(0, ________),   (2,________) 
How many ordered pairs satisfy both equations?
 __________ Name the pair(s). __________

Accepted Answer

The answer of Refer to the illustration. 
 
How many...

Question 11

The sum of the angles in any triangle is $5 ^ { x } = 9$ . In triangle ABC , angle A is $- 0.5579$ less than the sum of angles B and C , and angle C is $- 1.7925$ less than twice angle B . Find each angle.

Accepted Answer

A)  $v ^ { - 3 }$ 
B)  $( - 2 , - 12 )$ 
C)  $9 x ^ { 2 } - 24 x + 15$ 
D)  $3 x ^ { 2 } - 3$ 
E)  $x = 4$ 
A)  $v ^ { - 3 }$ 
B)  $( - 2 , - 12 )$ 
C)  $9 x ^ { 2 } - 24 x + 15$ 
D)  $3 x ^ { 2 } - 3$ 
E)  $x = 4$

Question 12

Tell whether the ordered pair (3,-2) is a solution of the system of equations. $\left\{ \begin{array} { l } 
y + 1 = \frac { 1 } { 3 } x \
2 x + 3 y = 0
\end{array} \right.$

Accepted Answer

The answer of Tell whether the ordered pair (3,-2) is...

Question 13

Use matrices to solve the system of equations. $\left\{ \begin{array} { l } 
x + y + z = 6 \
x + 3 y + z = 8 \
x + y + 3 z = 12
\end{array} \right.$

Accepted Answer

A)  $( 1,2,3 )$ 
B)  $( - 2 , - 1 , - 3 )$ 
C)  $( 2,1,3 )$ 
D)  no solution 
E)  infinitely many solutions 
A)  $( 1,2,3 )$ 
B)  $( - 2 , - 1 , - 3 )$ 
C)  $( 2,1,3 )$ 
D)  no solution 
E)  infinitely many solutions

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. $\left\{ \begin{array} { l } 
2 x + 2 y = 6 \
- x - y = - 3
\end{array} \right.$

Accepted Answer

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

Question 15

Use Cramer s rule to solve the system of equations, if possible. $\left\{ \begin{array} { l } 
5 x + 4 y = 0 \
10 x - 8 y = - 4
\end{array} \right.$

Accepted Answer

A)  $\left( - \frac { 1 } { 5 } , \frac { 1 } { 4 } \right)$ 
B)  $\left( - \frac { 1 } { 4 } , \frac { 1 } { 5 } \right)$ 
C)  (-5,4) 
D)  dependent 
E)  inconsistent 
A)  $\left( - \frac { 1 } { 5 } , \frac { 1 } { 4 } \right)$ 
B)  $\left( - \frac { 1 } { 4 } , \frac { 1 } { 5 } \right)$ 
C)  (-5,4) 
D)  dependent 
E)  inconsistent

Question 16

Use matrices to solve the system of equations. If the equations of the system are dependent, or if the system is inconsistent, so indicate. $\left\{ \begin{array} { c } 
x - 3 y = 5 \
- 2 x + 6 y = 10
\end{array} \right.$

Accepted Answer

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

Question 17

Use Cramer s rule to solve the system of equations, if possible. $\left\{ \begin{array} { l } 
x - y = 8 \
2 x + y = 7
\end{array} \right.$

Accepted Answer

A)  (5,3) 
B)  (-3,5) 
C)  (5,-3) 
D)  dependent 
E)  inconsistent 
A)  (5,3) 
B)  (-3,5) 
C)  (5,-3) 
D)  dependent 
E)  inconsistent

Question 18

Which of the following ordered pairs is a solution of the system $\left\{ \begin{array} { l } 
4 x - 6 y = 15 \
8 x + 2 y = 2
\end{array} \right.$ .

Accepted Answer

A)  $\left( 2 , - \frac { 1 } { 2 } \right)$ 
B)  $\left( 0 , - \frac { 7 } { 3 } \right)$ 
C)  $\left( \frac { 3 } { 4 } , - 2 \right)$ 
D)  $( 1,3 )$ 
A)  $\left( 2 , - \frac { 1 } { 2 } \right)$ 
B)  $\left( 0 , - \frac { 7 } { 3 } \right)$ 
C)  $\left( \frac { 3 } { 4 } , - 2 \right)$ 
D)  $( 1,3 )$

Question 19

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

Accepted Answer

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

Question 20

Consider the system $\left\{ \begin{array} { l } 
3 x + B y = 5 \
2 x - 5 y = - 3
\end{array} \right.$ . In order for this system to be inconsistent, what does the value of B need to be?

Accepted Answer

The answer of Consider the system \(\left\{ \begin{array} { l...

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

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

Suppose a hammer can be manufactured in two different ways. The number of hammers that will cost equal amounts to produce either way is called the ________ point.

Which of the following is a 2×3 matrix?

When three planes coincide, the equations of the system are ___________, and there are infinitely many solutions.

Each number in a matrix is called a(n) __________ or entry of the matrix.

Use Cramer s rule to solve the system of equations, if possible. $\left\{ \begin{array} { l } 2 x + y + z = 6 \\x - 2 y + 3 z = 8 \\x + y - 4 z = - 2\end{array} \right.$

Find the y -coordinate of the solution of the system $\left\{ \begin{array} { l } x - y - 2 z = 15 \\3 x + 2 y - z = 20 \\x - y + z = 9\end{array} \right.$

The sum of the angles in any triangle is $5 ^ { x } = 9$ . In triangle ABC , angle A is $- 0.5579$ less than the sum of angles B and C , and angle C is $- 1.7925$ less than twice angle B . Find each angle.

Tell whether the ordered pair (3,-2) is a solution of the system of equations. $\left\{ \begin{array} { l } y + 1 = \frac { 1 } { 3 } x \\2 x + 3 y = 0\end{array} \right.$

Use matrices to solve the system of equations. $\left\{ \begin{array} { l } x + y + z = 6 \\x + 3 y + z = 8 \\x + y + 3 z = 12\end{array} \right.$

Use matrices to solve the system of equations. If the equations of the system are dependent, or if the system is inconsistent, so indicate. $\left\{ \begin{array} { l } 2 x + 2 y = 6 \\- x - y = - 3\end{array} \right.$

Use Cramer s rule to solve the system of equations, if possible. $\left\{ \begin{array} { l } 5 x + 4 y = 0 \\10 x - 8 y = - 4\end{array} \right.$

Use matrices to solve the system of equations. If the equations of the system are dependent, or if the system is inconsistent, so indicate. $\left\{ \begin{array} { c } x - 3 y = 5 \\- 2 x + 6 y = 10\end{array} \right.$

Use Cramer s rule to solve the system of equations, if possible. $\left\{ \begin{array} { l } x - y = 8 \\2 x + y = 7\end{array} \right.$

Which of the following ordered pairs is a solution of the system $\left\{ \begin{array} { l } 4 x - 6 y = 15 \\8 x + 2 y = 2\end{array} \right.$ .

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

Consider the system $\left\{ \begin{array} { l } 3 x + B y = 5 \\2 x - 5 y = - 3\end{array} \right.$ . In order for this system to be inconsistent, what does the value of B need to be?

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

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

Suppose a hammer can be manufactured in two different ways. The number of hammers that will cost equal amounts to produce either way is called the ________ point.

Which of the following is a 2×3 matrix?

When three planes coincide, the equations of the system are ___________, and there are infinitely many solutions.

Each number in a matrix is called a(n) __________ or entry of the matrix.

Use Cramer s rule to solve the system of equations, if possible. {2x+y+z=6x−2y+3z=8x+y−4z=−2\left\{ \begin{array} { l } 2 x + y + z = 6 \\x - 2 y + 3 z = 8 \\x + y - 4 z = - 2\end{array} \right.⎩⎨⎧​2x+y+z=6x−2y+3z=8x+y−4z=−2​

Find the y -coordinate of the solution of the system {x−y−2z=153x+2y−z=20x−y+z=9\left\{ \begin{array} { l } x - y - 2 z = 15 \\3 x + 2 y - z = 20 \\x - y + z = 9\end{array} \right.⎩⎨⎧​x−y−2z=153x+2y−z=20x−y+z=9​

The sum of the angles in any triangle is 5x=95 ^ { x } = 95x=9 . In triangle ABC , angle A is −0.5579- 0.5579−0.5579 less than the sum of angles B and C , and angle C is −1.7925- 1.7925−1.7925 less than twice angle B . Find each angle.

Tell whether the ordered pair (3,-2) is a solution of the system of equations. {y+1=13x2x+3y=0\left\{ \begin{array} { l } y + 1 = \frac { 1 } { 3 } x \\2 x + 3 y = 0\end{array} \right.{y+1=31​x2x+3y=0​

Use matrices to solve the system of equations. {x+y+z=6x+3y+z=8x+y+3z=12\left\{ \begin{array} { l } x + y + z = 6 \\x + 3 y + z = 8 \\x + y + 3 z = 12\end{array} \right.⎩⎨⎧​x+y+z=6x+3y+z=8x+y+3z=12​

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+2y=6−x−y=−3\left\{ \begin{array} { l } 2 x + 2 y = 6 \\- x - y = - 3\end{array} \right.{2x+2y=6−x−y=−3​

Use Cramer s rule to solve the system of equations, if possible. {5x+4y=010x−8y=−4\left\{ \begin{array} { l } 5 x + 4 y = 0 \\10 x - 8 y = - 4\end{array} \right.{5x+4y=010x−8y=−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. {x−3y=5−2x+6y=10\left\{ \begin{array} { c } x - 3 y = 5 \\- 2 x + 6 y = 10\end{array} \right.{x−3y=5−2x+6y=10​

Use Cramer s rule to solve the system of equations, if possible. {x−y=82x+y=7\left\{ \begin{array} { l } x - y = 8 \\2 x + y = 7\end{array} \right.{x−y=82x+y=7​

Which of the following ordered pairs is a solution of the system {4x−6y=158x+2y=2\left\{ \begin{array} { l } 4 x - 6 y = 15 \\8 x + 2 y = 2\end{array} \right.{4x−6y=158x+2y=2​ .

Solve the system by elimination if possible. If the equations of the system are dependent, or if the system is inconsistent, so indicate. iii

Consider the system {3x+By=52x−5y=−3\left\{ \begin{array} { l } 3 x + B y = 5 \\2 x - 5 y = - 3\end{array} \right.{3x+By=52x−5y=−3​ . In order for this system to be inconsistent, what does the value of B need to be?

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

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

Use Cramer s rule to solve the system of equations, if possible. $\left\{ \begin{array} { l } 2 x + y + z = 6 \\x - 2 y + 3 z = 8 \\x + y - 4 z = - 2\end{array} \right.$

Find the y -coordinate of the solution of the system $\left\{ \begin{array} { l } x - y - 2 z = 15 \\3 x + 2 y - z = 20 \\x - y + z = 9\end{array} \right.$

The sum of the angles in any triangle is $5 ^ { x } = 9$ . In triangle ABC , angle A is $- 0.5579$ less than the sum of angles B and C , and angle C is $- 1.7925$ less than twice angle B . Find each angle.

Tell whether the ordered pair (3,-2) is a solution of the system of equations. $\left\{ \begin{array} { l } y + 1 = \frac { 1 } { 3 } x \\2 x + 3 y = 0\end{array} \right.$

Use matrices to solve the system of equations. $\left\{ \begin{array} { l } x + y + z = 6 \\x + 3 y + z = 8 \\x + y + 3 z = 12\end{array} \right.$

Use matrices to solve the system of equations. If the equations of the system are dependent, or if the system is inconsistent, so indicate. $\left\{ \begin{array} { l } 2 x + 2 y = 6 \\- x - y = - 3\end{array} \right.$

Use Cramer s rule to solve the system of equations, if possible. $\left\{ \begin{array} { l } 5 x + 4 y = 0 \\10 x - 8 y = - 4\end{array} \right.$

Use matrices to solve the system of equations. If the equations of the system are dependent, or if the system is inconsistent, so indicate. $\left\{ \begin{array} { c } x - 3 y = 5 \\- 2 x + 6 y = 10\end{array} \right.$

Use Cramer s rule to solve the system of equations, if possible. $\left\{ \begin{array} { l } x - y = 8 \\2 x + y = 7\end{array} \right.$

Which of the following ordered pairs is a solution of the system $\left\{ \begin{array} { l } 4 x - 6 y = 15 \\8 x + 2 y = 2\end{array} \right.$ .

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

Consider the system $\left\{ \begin{array} { l } 3 x + B y = 5 \\2 x - 5 y = - 3\end{array} \right.$ . In order for this system to be inconsistent, what does the value of B need to be?