Question 1

Solve the system. $$\left( \begin{array} { r l } 
x - 2 y + z & = 13 \
2 x + 3 y - 4 z & = - 14 \
- 2 x - 4 y + 2 z & = 14
\end{array} \right)$$

Accepted Answer

The answer of Solve the system. \[\left( \begin{array} { r...

Question 2

Use Cramer s rule to find the solution set for the system. $\left(\begin{array}{l}
x&-&y&-&5 z&=&-8 \
5 x&+&6 y&-&7 z&=&-15 \
-x&+&5 y&-&z&=&-8
\end{array}\right)$ If the equations of the system are dependent, or if a system is inconsistent, so indicate. In those cases enter dependent or inconsistent .

Accepted Answer

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

Question 3

Solve the homogeneous system. $$\left( \begin{array} { r } 
x - 2 y + 13 z = 0 \
7 x + y - 6 z = 0 \
8 x - y + 7 z = 0
\end{array} \right)$$ If the equations of the system are dependent, or if a system is inconsistent, so indicate. In those cases enter dependent or inconsistent .

Accepted Answer

The answer of Solve the homogeneous system. \[\left( \begin{array} {...

Question 4

Use Cramer s rule to find the solution set for the system. $$\left( \begin{array} { l } 
5 x + 3 y = 10 \
4 x - 3 y = 35
\end{array} \right)$$ If the equations of the system are dependent, or if a system is inconsistent, so indicate. In those cases enter dependent or inconsistent . Otherwise, enter your answer in the form ( x , y ).

Accepted Answer

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

Question 5

Every system of nonlinear equations has either one solution, infinitely many solutions, or no solution.

Accepted Answer

A) True 
 B)False

Question 6

Solve the system by the substitution or elimination method. $$\left( \begin{array} { r l } 
x ^ { 2 } + y ^ { 2 } & = 44 \
x - y & = 10
\end{array} \right)$$

Accepted Answer

A)  $( 5 + i \sqrt { 3 } , - 5 + i \sqrt { 3 } ) , ( 5 - i \sqrt { 3 } , - 5 - i \sqrt { 3 } )$ 
B)  $( 5 - i \sqrt { 3 } , - 5 + i \sqrt { 3 } ) , ( 5 + i \sqrt { 3 } , - 5 - i \sqrt { 3 } )$ 
C)  $( 5 + i \sqrt { 3 } , - 5 + i \sqrt { 3 } )$ 
D)  $( 5 - i \sqrt { 3 } , - 5 - i \sqrt { 3 } )$ 
A)  $( 5 + i \sqrt { 3 } , - 5 + i \sqrt { 3 } ) , ( 5 - i \sqrt { 3 } , - 5 - i \sqrt { 3 } )$ 
B)  $( 5 - i \sqrt { 3 } , - 5 + i \sqrt { 3 } ) , ( 5 + i \sqrt { 3 } , - 5 - i \sqrt { 3 } )$ 
C)  $( 5 + i \sqrt { 3 } , - 5 + i \sqrt { 3 } )$ 
D)  $( 5 - i \sqrt { 3 } , - 5 - i \sqrt { 3 } )$

Question 7

Use Cramer s rule to find the solution set for the system. $$\left( \begin{array} { c l c c c } 
x-4 y+5 z & =9 \
-4 x+8 y-5 z & =-16 \
9 x-12 y+10 z & =33
\end{array} \right)$$ If the equations of the system are dependent, or if a system is inconsistent, so indicate. In those cases enter dependent or inconsistent .

Accepted Answer

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

Question 8

Solve the system by the substitution or elimination method. $$\left( \begin{array} { l } 
5 x ^ { 2 } + y ^ { 2 } = 20 \
x ^ { 2 } + y ^ { 2 } = 4
\end{array} \right)$$ Express your answer as an ordered pair. If there is more than one solution, separate your answers with a comma.

Accepted Answer

The answer of Solve the system by the substitution or...

Question 9

Evaluate $2 \times 2$ determinant. $$\left| \begin{array} { l l } 
4 & 2 \
1 & 5
\end{array} \right|$$

Accepted Answer

A)  22 
B)  13 
C)  18 
A)  22 
B)  13 
C)  18

Question 10

Evaluate $2 \times 2$ determinant. $$\left| \begin{array} { r r } 
- 2 & - 5 \
- 1 & - 9
\end{array} \right|$$

Accepted Answer

A)  13 
B)  20 
C)  -5 
A)  13 
B)  20 
C)  -5

Question 11

Solve the system by the substitution or elimination method. $$\left( \begin{array} { l } 
y = x ^ { 2 } + 6 x + 4 \
2 x + y = - 3
\end{array} \right)$$

Accepted Answer

A)  (-1, 1), (7, 11) 
B)  (1, -1), (-7, -11) 
C)  (1, -1), (7, 11) 
D)  (-1, -1), (-7, 11) 
A)  (-1, 1), (7, 11) 
B)  (1, -1), (-7, -11) 
C)  (1, -1), (7, 11) 
D)  (-1, -1), (-7, 11)

Question 12

Solve the system. $$\left( \begin{array} { r l c } 
x + 5 y - 4 z & = & - 10 \
5 y - z & = & 6 \
3 y + 3 z & = & 18
\end{array} \right)$$

Accepted Answer

The answer of Solve the system. \[\left( \begin{array} { r...

Question 13

Change the augmented matrix of the system to reduced echelon form and then indicate the solutions of the system. $$\left( \begin{array} { r } 
2 x - 4 y + 3 z = 4 \
3 x + 5 y - z = 3
\end{array} \right)$$ Use k to express any real number. Enter your answer in the form ( x ( k ), y ( k ), k ).

Accepted Answer

The answer of Change the augmented matrix of the system...

Question 14

The matrix is the reduced echelon matrix for a system with variables x 1 , x 2 , x 3 , and x 4 . Find the solution set of the system. $$\left[ \begin{array} { l l l l | r } 
1 & 0 & 0 & 0 & - 3 \
0 & 1 & 0 & 0 & - 3 \
0 & 0 & 1 & 0 & 15 \
0 & 0 & 0 & 1 & - 6
\end{array} \right]$$

Accepted Answer

A)  ( $-$ 3, $-$ 3, 15, $-$ 6) 
B)  ( $-$ 3, $-$ 1, 15, $-$ 3) 
C)  (0, $-$ 3, 15, $-$ 8) 
D)  ( $-$ 6, $-$ 1, 17, $-$ 3) 
E)  inconsistent 
A)  ( $-$ 3, $-$ 3, 15, $-$ 6) 
B)  ( $-$ 3, $-$ 1, 15, $-$ 3) 
C)  (0, $-$ 3, 15, $-$ 8) 
D)  ( $-$ 6, $-$ 1, 17, $-$ 3) 
E)  inconsistent

Question 15

Use Cramer s rule to find the solution set for the system. $$\left( \begin{array} { c c c c } 
3 x - 3 y & = & - 12 \
- x + 2 y & = & 9
\end{array} \right)$$ If the equations of the system are dependent, or if a system is inconsistent, so indicate. In those cases enter dependent or inconsistent . Otherwise, enter your answer in the form ( x , y ).

Accepted Answer

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

Question 16

Use a matrix approach to solve the system. $$\left( \begin{array} { r } 
2 x + 2 y - z = 8 \
3 x + 3 y + 4 z = 1 \
5 x + y + 4 z = 7
\end{array} \right)$$ If a system is inconsistent, so indicate. In those cases enter inconsistent . Otherwise, enter your answer in the form ( x , y ).

Accepted Answer

The answer of Use a matrix approach to solve the...

Question 17

Solve the system by using either the substitution method or the elimination-by-addition method, whichever seems more appropriate. $\left( \begin{array} { c c c c } 
x &+& y & = & 1,100 \
0.96 x &+ &0.29 y & = & 654
\end{array} \right)$ If the equations of the system are dependent, or if a system is inconsistent, so indicate. In those cases enter dependent or inconsistent . Otherwise, enter your answer as an ordered pair ( x , y ).

Accepted Answer

The answer of Solve the system by using either the...

Question 18

Use Cramer s rule to find the solution set for the system. $$\left( \begin{array} { r l } 
2 x - 3 y & = - 13 \
y & = 5
\end{array} \right)$$ If the equations of the system are dependent, or if a system is inconsistent, so indicate. In those cases enter dependent or inconsistent . Otherwise, enter your answer in the form ( x , y ).

Accepted Answer

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

Question 19

Solve the system by using either the substitution method or the elimination-by-addition method, whichever seems more appropriate. $\left( \begin{array} { l } 
x = 3 y + 3 \
x = - 4 y + 5
\end{array} \right)$

Accepted Answer

A)  $\left( \frac { 31 } { 7 } , \frac { 2 } { 7 } \right)$ 
B)  $\left( \frac { 31 } { 7 } , - \frac { 2 } { 7 } \right)$ 
C)  $\left( \frac { 27 } { 7 } , \frac { 2 } { 7 } \right)$ 
D)  $\left( \frac { 29 } { 7 } , \frac { 2 } { 7 } \right)$ 
E)  $\left( \frac { 27 } { 7 } , - \frac { 2 } { 7 } \right)$ 
A)  $\left( \frac { 31 } { 7 } , \frac { 2 } { 7 } \right)$ 
B)  $\left( \frac { 31 } { 7 } , - \frac { 2 } { 7 } \right)$ 
C)  $\left( \frac { 27 } { 7 } , \frac { 2 } { 7 } \right)$ 
D)  $\left( \frac { 29 } { 7 } , \frac { 2 } { 7 } \right)$ 
E)  $\left( \frac { 27 } { 7 } , - \frac { 2 } { 7 } \right)$

Question 20

Solve the system. $\begin{array}{l}
(4 x+3 y-3 z=29) \
x-5 z=12 \
5 x+5 z=0 \
\end{array}$

Accepted Answer

A)  x = 2, y = 5, z = -2 
B)  x = 3, y = 5, z = -3 
C)  x = 3, y = 4, z = -2 
D)  x = 2, y = 6, z = -3 
A)  x = 2, y = 5, z = -2 
B)  x = 3, y = 5, z = -3 
C)  x = 3, y = 4, z = -2 
D)  x = 2, y = 6, z = -3

Solve the system. $\left( \begin{array} { r l } x - 2 y + z & = 13 \\2 x + 3 y - 4 z & = - 14 \\- 2 x - 4 y + 2 z & = 14\end{array} \right)$

Solve the homogeneous system. $\left( \begin{array} { r } x - 2 y + 13 z = 0 \\7 x + y - 6 z = 0 \\8 x - y + 7 z = 0\end{array} \right)$ If the equations of the system are dependent, or if a system is inconsistent, so indicate. In those cases enter dependent or inconsistent .

Every system of nonlinear equations has either one solution, infinitely many solutions, or no solution.

Solve the system by the substitution or elimination method. $\left( \begin{array} { r l } x ^ { 2 } + y ^ { 2 } & = 44 \\x - y & = 10\end{array} \right)$

Solve the system by the substitution or elimination method. $\left( \begin{array} { l } 5 x ^ { 2 } + y ^ { 2 } = 20 \\x ^ { 2 } + y ^ { 2 } = 4\end{array} \right)$ Express your answer as an ordered pair. If there is more than one solution, separate your answers with a comma.

Evaluate $2 \times 2$ determinant. $\left| \begin{array} { l l } 4 & 2 \\1 & 5\end{array} \right|$

Evaluate $2 \times 2$ determinant. $\left| \begin{array} { r r } - 2 & - 5 \\- 1 & - 9\end{array} \right|$

Solve the system by the substitution or elimination method. $\left( \begin{array} { l } y = x ^ { 2 } + 6 x + 4 \\2 x + y = - 3\end{array} \right)$

Solve the system. $\left( \begin{array} { r l c } x + 5 y - 4 z & = & - 10 \\5 y - z & = & 6 \\3 y + 3 z & = & 18\end{array} \right)$

Change the augmented matrix of the system to reduced echelon form and then indicate the solutions of the system. $\left( \begin{array} { r } 2 x - 4 y + 3 z = 4 \\3 x + 5 y - z = 3\end{array} \right)$ Use k to express any real number. Enter your answer in the form ( x ( k ), y ( k ), k ).

The matrix is the reduced echelon matrix for a system with variables x 1 , x 2 , x 3 , and x 4 . Find the solution set of the system. $\left[ \begin{array} { l l l l | r } 1 & 0 & 0 & 0 & - 3 \\0 & 1 & 0 & 0 & - 3 \\0 & 0 & 1 & 0 & 15 \\0 & 0 & 0 & 1 & - 6\end{array} \right]$

Use a matrix approach to solve the system. $\left( \begin{array} { r } 2 x + 2 y - z = 8 \\3 x + 3 y + 4 z = 1 \\5 x + y + 4 z = 7\end{array} \right)$ If a system is inconsistent, so indicate. In those cases enter inconsistent . Otherwise, enter your answer in the form ( x , y ).

Solve the system by using either the substitution method or the elimination-by-addition method, whichever seems more appropriate. $\left( \begin{array} { l } x = 3 y + 3 \\x = - 4 y + 5\end{array} \right)$

Solve the system. (4x+3y-3z=29) x-5z=12 5x+5z=0

Some Basic Concepts of Arithmetic and Algebra

The Real Numbers

Equations, Inequalities and Problem Solving

Formulas and Problem Solving

Coordinate Geometry and Linear Systems

Exponents and Polynomials

Factoring, Solving Equations and Problem Solving

A Transition From Elementary Algebra to Intermediate Algebra

Rational Expressions

Exponents and Radicals

Quadratic Equations and Inequalities

Coordinate Geometry: Lines, Parabolas, Circles, Ellipses and Hyperbolas

Functions

Exponential and Logarithmic Functions

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Exam 15: Systems of Equations: Matrices and Determinants

Solve the system. (x−2y+z=132x+3y−4z=−14−2x−4y+2z=14)\left( \begin{array} { r l } x - 2 y + z & = 13 \\2 x + 3 y - 4 z & = - 14 \\- 2 x - 4 y + 2 z & = 14\end{array} \right)​x−2y+z2x+3y−4z−2x−4y+2z​=13=−14=14​​

Every system of nonlinear equations has either one solution, infinitely many solutions, or no solution.

Solve the system by the substitution or elimination method. (x2+y2=44x−y=10)\left( \begin{array} { r l } x ^ { 2 } + y ^ { 2 } & = 44 \\x - y & = 10\end{array} \right)(x2+y2x−y​=44=10​)

Evaluate 2×22 \times 22×2 determinant. ∣4215∣\left| \begin{array} { l l } 4 & 2 \\1 & 5\end{array} \right|​41​25​​

Evaluate 2×22 \times 22×2 determinant. ∣−2−5−1−9∣\left| \begin{array} { r r } - 2 & - 5 \\- 1 & - 9\end{array} \right|​−2−1​−5−9​​

Solve the system by the substitution or elimination method. (y=x2+6x+42x+y=−3)\left( \begin{array} { l } y = x ^ { 2 } + 6 x + 4 \\2 x + y = - 3\end{array} \right)(y=x2+6x+42x+y=−3​)

Solve the system. (x+5y−4z=−105y−z=63y+3z=18)\left( \begin{array} { r l c } x + 5 y - 4 z & = & - 10 \\5 y - z & = & 6 \\3 y + 3 z & = & 18\end{array} \right)​x+5y−4z5y−z3y+3z​===​−10618​​

Solve the system by using either the substitution method or the elimination-by-addition method, whichever seems more appropriate. (x=3y+3x=−4y+5)\left( \begin{array} { l } x = 3 y + 3 \\x = - 4 y + 5\end{array} \right)(x=3y+3x=−4y+5​)

Solve the system. (4x+3y-3z=29) x-5z=12 5x+5z=0

Some Basic Concepts of Arithmetic and Algebra

The Real Numbers

Equations, Inequalities and Problem Solving

Formulas and Problem Solving

Coordinate Geometry and Linear Systems

Exponents and Polynomials

Factoring, Solving Equations and Problem Solving

A Transition From Elementary Algebra to Intermediate Algebra

Rational Expressions

Exponents and Radicals

Quadratic Equations and Inequalities

Coordinate Geometry: Lines, Parabolas, Circles, Ellipses and Hyperbolas

Functions

Exponential and Logarithmic Functions

Filters

Solve the system. $\left( \begin{array} { r l } x - 2 y + z & = 13 \\2 x + 3 y - 4 z & = - 14 \\- 2 x - 4 y + 2 z & = 14\end{array} \right)$

Solve the system by the substitution or elimination method. $\left( \begin{array} { r l } x ^ { 2 } + y ^ { 2 } & = 44 \\x - y & = 10\end{array} \right)$

Evaluate $2 \times 2$ determinant. $\left| \begin{array} { l l } 4 & 2 \\1 & 5\end{array} \right|$

Evaluate $2 \times 2$ determinant. $\left| \begin{array} { r r } - 2 & - 5 \\- 1 & - 9\end{array} \right|$

Solve the system by the substitution or elimination method. $\left( \begin{array} { l } y = x ^ { 2 } + 6 x + 4 \\2 x + y = - 3\end{array} \right)$

Solve the system. $\left( \begin{array} { r l c } x + 5 y - 4 z & = & - 10 \\5 y - z & = & 6 \\3 y + 3 z & = & 18\end{array} \right)$

Solve the system by using either the substitution method or the elimination-by-addition method, whichever seems more appropriate. $\left( \begin{array} { l } x = 3 y + 3 \\x = - 4 y + 5\end{array} \right)$