Solve the system by elimination. -\[\begin{array} { l } x + 9 y = - 55 \\ 8 x + 8 y = 8 \end{array}\]

A) $\{ ( 8 , - 7 ) \}$ B) $\{ ( - 8 , - 6 ) \}$ C) $\{ ( 7 , - 6 ) \}$ D) $\varnothing$ A) $\{ ( 8 , - 7 ) \}$ B) $\{ ( - 8 , - 6 ) \}$ C) $\{ ( 7 , - 6 ) \}$ D) $\varnothing$

Solve the system by using the inverse of the coefficient matrix. -\[\begin{array} { l } 3 x + y - 2 z - w = 8 \\ - x + 2 y + z - 4 w = - 12 \\ 2 x - 2 y + 3 z + w = 8 \\ - 2 x - y - z - 4 w = - 7 \end{array}\]

A) $\{ ( 3,2,1 , - 1 ) \}$ B) $\{ ( 3 , - 2 , - 1,1 ) \}$ C) $\{ ( 1 , - 3 , - 2 , - 1 ) \}$ D) $\varnothing$ A) $\{ ( 3,2,1 , - 1 ) \}$ B) $\{ ( 3 , - 2 , - 1,1 ) \}$ C) $\{ ( 1 , - 3 , - 2 , - 1 ) \}$ D) $\varnothing$

Solve the system by elimination. -\[\begin{array} { c } 9 x - 6 y = - 42 \\ - 3 x - 2 y = - 14 \end{array}\]

A) $\varnothing$ B) $\{ ( 0,8 ) \}$ C) $\{ ( 0,7 ) \}$ D) $\{ ( - 1,8 ) \}$ A) $\varnothing$ B) $\{ ( 0,8 ) \}$ C) $\{ ( 0,7 ) \}$ D) $\{ ( - 1,8 ) \}$

If the system has infinitely many solutions, write the solution set with x arbitrary. -\[\begin{array} { l } \frac { 2 } { x } - \frac { 1 } { y } - \frac { 2 } { z } = - \frac { 53 } { 20 } \\ - \frac { 1 } { x } + \frac { 3 } { y } + \frac { 7 } { z } = \frac { 63 } { 20 } \\ \frac { 3 } { x } - \frac { 1 } { y } - \frac { 1 } { z } = - \frac { 69 } { 20 } \end{array}\]

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

Find the cofactor of the indicated element. - a 21 \[\begin{array} { l } \left| \begin{array} { r r r } 5 & 3 & 4 \\ - 3 & 0 & 1 \\ 3 & 4 & 5 \end{array} \right| \end{array}\]

A) 1 B) 11 C) $- 1$ D) $- 11$ A) 1 B) 11 C) $- 1$ D) $- 11$

Exam 10: Systems and Matrices

A nonlinear system is given, along with the graphs of both equations in the system. Determine if the points of intersection specified on the graph are solutions of the system by substituting directly into both equations. - y=x -=7 $A nonlinear system is given, along with the graphs of both equations in the system. Determine if the points of intersection specified on the graph are solutions of the system by substituting directly into both equations. - \begin{array} { l } y = \ln x \\ x ^ { 2 } - y ^ { 2 } = 7 \end{array}$

(Multiple Choice)

4.7/5

(48)

Question 361

Solve the system by elimination. - x+9y=-55 8x+8y=8

(Multiple Choice)

4.7/5

(30)

Question 362

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, let the last variable be the arbitrary variable. - 4x-y+5z=71 6x+9y+3z=123 8x-9y+z=35

(Multiple Choice)

4.8/5

(37)

Question 363

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, let the last variable be the arbitrary variable. - x+3y-2z-w=18 4x+y+z+2w=22 -3x-y-3z-2w=-11 x-y-3z-2w=1

(Multiple Choice)

4.9/5

(36)

Question 364

Solve the system by using the inverse of the coefficient matrix. - 3x+y-2z-w=8 -x+2y+z-4w=-12 2x-2y+3z+w=8 -2x-y-z-4w=-7

(Multiple Choice)

4.8/5

(38)

Question 365

Find the inverse, if it exists, for the matrix. - $\left[ \begin{array} { r r r r } 0 & 5 & 0 & - 3 \\4 & 15 & - 3 & - 6 \\8 & 10 & - 6 & - 3 \\12 & 0 & - 6 & 0\end{array} \right]$

(Multiple Choice)

4.8/5

(36)

Question 366

Solve the system by elimination. - 9x-6y=-42 -3x-2y=-14

(Multiple Choice)

5.0/5

(39)

Question 367

Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth. -Find the dimensions of a rectangular garden with perimeter $62 \mathrm { yd }$ and area $220 \mathrm { yd } ^ { 2 }$ .

(Multiple Choice)

4.8/5

(42)

Question 368

If the system has infinitely many solutions, write the solution set with x arbitrary. - --=- -++= --=-

(Multiple Choice)

4.9/5

(30)

Question 369

Use a graphing calcula tor to find the inverse of the matrix. Give five decimal places, if necessary. - $A = \left[ \begin{array} { c c c } 1.52 & 5.55 & 4 \\- 0.63 & 7.33 & 3.21 \\8.2 & 0.003 & - 2.8\end{array} \right]$

(Multiple Choice)

4.7/5

(36)

Question 370

Which method should be used to solve the system? Explain your answer, including a description of the first step. - +3=100 -7+5=4

(Essay)

4.9/5

(37)

Question 371

Find the indicated matrix. -Let $C = \left[ \begin{array} { r } 4 \\ - 2 \\ 8 \end{array} \right]$ . Find $\frac { 1 } { 2 } C$ .

(Multiple Choice)

4.8/5

(35)

Question 372

Solve the problem using matrices. -Jerry has three pieces of string. The total length is $91 \mathrm {~cm}$ . The sum of the two longer pieces is $76 \mathrm {~cm}$ . The middle piece is twice as long as the shortest piece. What are the lengths of the three pieces?

(Multiple Choice)

4.9/5

(35)

Question 373

Decide whether or not the matrices are inverses of each other. - $\left[ \begin{array} { r r } 6 & - 5 \\- 3 & 5\end{array} \right] \text { and } \left[ \begin{array} { c c } \frac { 1 } { 3 } & \frac { 1 } { 3 } \\\frac { 1 } { 5 } & \frac { 2 } { 5 }\end{array} \right]$

(Multiple Choice)

4.9/5

(28)

Question 374

Use the given row transformation to change the matrix as indicated. - $\left[ \begin{array} { r r r } 3 & 5 & 4 \\ - 6 & 3 & - 1 \\ 7 & 4 & 0 \end{array} \right] ; 2$ times row 1 added to row 2

(Multiple Choice)

4.8/5

(40)

Question 375

Provide an appropriate response. -Which one of the following is a description of the graph of the inequality? $( x - 1 ) ^ { 2 } + ( y - 3 ) ^ { 2 } < 16$

(Multiple Choice)

4.8/5

(31)

Question 376

Find the cofactor of the indicated element. - a 21 5 3 4 -3 0 1 3 4 5

(Multiple Choice)

4.7/5

(41)

Question 377

Graph the solution set of the system of inequalities. - -\geq1 y\geq|x-8| $Graph the solution set of the system of inequalities. - \begin{array}{l} \frac{x^{2}}{36}-\frac{y^{2}}{9} \geq 1 \\ y \geq|x-8| \end{array}$

(Multiple Choice)

4.7/5

(31)

Question 378

Use a graphing calculator to find the value of the determinant. - $\left| \begin{array} { r r r } 1 & 1 & - 3 \\5 & 5 & 5 \\4 & - 5 & - 3\end{array} \right|$

(Multiple Choice)

4.8/5

(40)

Question 379

Which method should be used to solve the system? Explain your answer, including a description of the first step. - $- 2 x - 5 y \leq - 10$ $Which method should be used to solve the system? Explain your answer, including a description of the first step. - - 2 x - 5 y \leq - 10$

(Multiple Choice)

4.8/5

(27)

Question 380

Showing 361 - 380 of 507

Solve the system by elimination. - x+9y=-55 8x+8y=8

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, let the last variable be the arbitrary variable. - 4x-y+5z=71 6x+9y+3z=123 8x-9y+z=35

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, let the last variable be the arbitrary variable. - x+3y-2z-w=18 4x+y+z+2w=22 -3x-y-3z-2w=-11 x-y-3z-2w=1

Solve the system by using the inverse of the coefficient matrix. - 3x+y-2z-w=8 -x+2y+z-4w=-12 2x-2y+3z+w=8 -2x-y-z-4w=-7

Find the inverse, if it exists, for the matrix. - $\left[ \begin{array} { r r r r } 0 & 5 & 0 & - 3 \\4 & 15 & - 3 & - 6 \\8 & 10 & - 6 & - 3 \\12 & 0 & - 6 & 0\end{array} \right]$

Solve the system by elimination. - 9x-6y=-42 -3x-2y=-14

Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth. -Find the dimensions of a rectangular garden with perimeter $62 \mathrm { yd }$ and area $220 \mathrm { yd } ^ { 2 }$ .

If the system has infinitely many solutions, write the solution set with x arbitrary. - --=- -++= --=-

Use a graphing calcula tor to find the inverse of the matrix. Give five decimal places, if necessary. - $A = \left[ \begin{array} { c c c } 1.52 & 5.55 & 4 \\- 0.63 & 7.33 & 3.21 \\8.2 & 0.003 & - 2.8\end{array} \right]$

Which method should be used to solve the system? Explain your answer, including a description of the first step. - +3=100 -7+5=4

Find the indicated matrix. -Let $C = \left[ \begin{array} { r } 4 \\ - 2 \\ 8 \end{array} \right]$ . Find $\frac { 1 } { 2 } C$ .

Solve the problem using matrices. -Jerry has three pieces of string. The total length is $91 \mathrm {~cm}$ . The sum of the two longer pieces is $76 \mathrm {~cm}$ . The middle piece is twice as long as the shortest piece. What are the lengths of the three pieces?

Decide whether or not the matrices are inverses of each other. - $\left[ \begin{array} { r r } 6 & - 5 \\- 3 & 5\end{array} \right] \text { and } \left[ \begin{array} { c c } \frac { 1 } { 3 } & \frac { 1 } { 3 } \\\frac { 1 } { 5 } & \frac { 2 } { 5 }\end{array} \right]$

Use the given row transformation to change the matrix as indicated. - $\left[ \begin{array} { r r r } 3 & 5 & 4 \\ - 6 & 3 & - 1 \\ 7 & 4 & 0 \end{array} \right] ; 2$ times row 1 added to row 2

Provide an appropriate response. -Which one of the following is a description of the graph of the inequality? $( x - 1 ) ^ { 2 } + ( y - 3 ) ^ { 2 } < 16$

Find the cofactor of the indicated element. - a 21 5 3 4 -3 0 1 3 4 5

Graph the solution set of the system of inequalities. - -\geq1 y\geq|x-8| $Graph the solution set of the system of inequalities. - \begin{array}{l} \frac{x^{2}}{36}-\frac{y^{2}}{9} \geq 1 \\ y \geq|x-8| \end{array}$

Use a graphing calculator to find the value of the determinant. - $\left| \begin{array} { r r r } 1 & 1 & - 3 \\5 & 5 & 5 \\4 & - 5 & - 3\end{array} \right|$

Which method should be used to solve the system? Explain your answer, including a description of the first step. - $- 2 x - 5 y \leq - 10$ $Which method should be used to solve the system? Explain your answer, including a description of the first step. - - 2 x - 5 y \leq - 10$

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Analytic Geometry

Further Topics in Algebra

Filters

Exam 10: Systems and Matrices

A nonlinear system is given, along with the graphs of both equations in the system. Determine if the points of intersection specified on the graph are solutions of the system by substituting directly into both equations. - y=x -=7

Solve the system by elimination. - x+9y=-55 8x+8y=8

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, let the last variable be the arbitrary variable. - 4x-y+5z=71 6x+9y+3z=123 8x-9y+z=35

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, let the last variable be the arbitrary variable. - x+3y-2z-w=18 4x+y+z+2w=22 -3x-y-3z-2w=-11 x-y-3z-2w=1

Solve the system by using the inverse of the coefficient matrix. - 3x+y-2z-w=8 -x+2y+z-4w=-12 2x-2y+3z+w=8 -2x-y-z-4w=-7

Find the inverse, if it exists, for the matrix. - [050−3415−3−6810−6−3120−60]\left[ \begin{array} { r r r r } 0 & 5 & 0 & - 3 \\4 & 15 & - 3 & - 6 \\8 & 10 & - 6 & - 3 \\12 & 0 & - 6 & 0\end{array} \right]​04812​515100​0−3−6−6​−3−6−30​​

Solve the system by elimination. - 9x-6y=-42 -3x-2y=-14

Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth. -Find the dimensions of a rectangular garden with perimeter 62yd62 \mathrm { yd }62yd and area 220yd2220 \mathrm { yd } ^ { 2 }220yd2 .

If the system has infinitely many solutions, write the solution set with x arbitrary. - --=- -++= --=-

Which method should be used to solve the system? Explain your answer, including a description of the first step. - +3=100 -7+5=4

Find the indicated matrix. -Let C=[4−28]C = \left[ \begin{array} { r } 4 \\ - 2 \\ 8 \end{array} \right]C=​4−28​​ . Find 12C\frac { 1 } { 2 } C21​C .

Solve the problem using matrices. -Jerry has three pieces of string. The total length is 91 cm91 \mathrm {~cm}91 cm . The sum of the two longer pieces is 76 cm76 \mathrm {~cm}76 cm . The middle piece is twice as long as the shortest piece. What are the lengths of the three pieces?

Use the given row transformation to change the matrix as indicated. - [354−63−1740];2\left[ \begin{array} { r r r } 3 & 5 & 4 \\ - 6 & 3 & - 1 \\ 7 & 4 & 0 \end{array} \right] ; 2​3−67​534​4−10​​;2 times row 1 added to row 2

Provide an appropriate response. -Which one of the following is a description of the graph of the inequality? (x−1)2+(y−3)2<16( x - 1 ) ^ { 2 } + ( y - 3 ) ^ { 2 } < 16(x−1)2+(y−3)2<16

Find the cofactor of the indicated element. - a 21 5 3 4 -3 0 1 3 4 5

Graph the solution set of the system of inequalities. - -\geq1 y\geq|x-8|

Use a graphing calculator to find the value of the determinant. - ∣11−35554−5−3∣\left| \begin{array} { r r r } 1 & 1 & - 3 \\5 & 5 & 5 \\4 & - 5 & - 3\end{array} \right|​154​15−5​−35−3​​

Which method should be used to solve the system? Explain your answer, including a description of the first step. - −2x−5y≤−10- 2 x - 5 y \leq - 10−2x−5y≤−10

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Analytic Geometry

Further Topics in Algebra

Filters

Find the inverse, if it exists, for the matrix. - $\left[ \begin{array} { r r r r } 0 & 5 & 0 & - 3 \\4 & 15 & - 3 & - 6 \\8 & 10 & - 6 & - 3 \\12 & 0 & - 6 & 0\end{array} \right]$

Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth. -Find the dimensions of a rectangular garden with perimeter $62 \mathrm { yd }$ and area $220 \mathrm { yd } ^ { 2 }$ .

Find the indicated matrix. -Let $C = \left[ \begin{array} { r } 4 \\ - 2 \\ 8 \end{array} \right]$ . Find $\frac { 1 } { 2 } C$ .

Solve the problem using matrices. -Jerry has three pieces of string. The total length is $91 \mathrm {~cm}$ . The sum of the two longer pieces is $76 \mathrm {~cm}$ . The middle piece is twice as long as the shortest piece. What are the lengths of the three pieces?

Use the given row transformation to change the matrix as indicated. - $\left[ \begin{array} { r r r } 3 & 5 & 4 \\ - 6 & 3 & - 1 \\ 7 & 4 & 0 \end{array} \right] ; 2$ times row 1 added to row 2

Provide an appropriate response. -Which one of the following is a description of the graph of the inequality? $( x - 1 ) ^ { 2 } + ( y - 3 ) ^ { 2 } < 16$

Graph the solution set of the system of inequalities. - -\geq1 y\geq|x-8| $Graph the solution set of the system of inequalities. - \begin{array}{l} \frac{x^{2}}{36}-\frac{y^{2}}{9} \geq 1 \\ y \geq|x-8| \end{array}$

Use a graphing calculator to find the value of the determinant. - $\left| \begin{array} { r r r } 1 & 1 & - 3 \\5 & 5 & 5 \\4 & - 5 & - 3\end{array} \right|$

Which method should be used to solve the system? Explain your answer, including a description of the first step. - $- 2 x - 5 y \leq - 10$ $Which method should be used to solve the system? Explain your answer, including a description of the first step. - - 2 x - 5 y \leq - 10$