Solve the system by the addition method. \[\begin{array} { l } \frac { 1 } { 4 } x + y = - \frac { 7 } { 5 } \\ x + 4 y = - 2.6 \end{array}\]

A) No solution; \{ \} ; inconsistent system B) $( 0 , - 0.65 )$ C) Infinitely many solutions; $\left\{ ( x , y ) \mid y = - \frac { 1 } { 4 } x - \frac { 7 } { 5 } \right\}$; dependent system D) $( 0 , - 1.4 )$ A) No solution; \{ \} ; inconsistent system B) $( 0 , - 0.65 )$ C) Infinitely many solutions; $\left\{ ( x , y ) \mid y = - \frac { 1 } { 4 } x - \frac { 7 } { 5 } \right\}$; dependent system D) $( 0 , - 1.4 )$

Determine which point is the solution to the given system. \[\begin{array} { l } y = - \frac { 7 } { 2 } x + 32 \\ y = \frac { 4 } { 5 } x - 11 \end{array}\]

A) (12, -10) B) (10, -3) C) (8, 4) D) (15, 1) A) (12, -10) B) (10, -3) C) (8, 4) D) (15, 1)

Set up the augmented matrix. \[\begin{array} { l } - 4 x + 5 y = - 8 \\ - 8 x + 5 y = 2 \end{array}\]

A) $\left[\begin{array}{cc|c} -4 & 5 & -8 \\ -8 & 5 & 2 \end{array}\right]$ B) $\left[\begin{array}{ll|l} -4 & 5 & 0 \\ -8 & 5 & 0 \end{array}\right]$ C) $\left[\begin{array}{cc} -4 & 5 \\ -8 & 5 \end{array}\right]$ D) $\left[\begin{array}{cc|c} -4 & -5 & -8 \\ 8 & 5 & 2 \end{array}\right]$ A) $\left[\begin{array}{cc|c} -4 & 5 & -8 \\ -8 & 5 & 2 \end{array}\right]$ B) $\left[\begin{array}{ll|l} -4 & 5 & 0 \\ -8 & 5 & 0 \end{array}\right]$ C) $\left[\begin{array}{cc} -4 & 5 \\ -8 & 5 \end{array}\right]$ D) $\left[\begin{array}{cc|c} -4 & -5 & -8 \\ 8 & 5 & 2 \end{array}\right]$

Solve the system by using the Gauss-Jordan method. \[\begin{aligned} - 5 x + 4 y & = - 14 \\ x - 3 y & = 16 \end{aligned}\]

A) $( 2 , - 1 )$ B) $( - 2 , - 6 )$ C) $\left( \frac { 458 } { 11 } , \frac { 94 } { 11 } \right)$ D) $\left( \frac { 106 } { 19 } , - \frac { 66 } { 19 } \right)$ A) $( 2 , - 1 )$ B) $( - 2 , - 6 )$ C) $\left( \frac { 458 } { 11 } , \frac { 94 } { 11 } \right)$ D) $\left( \frac { 106 } { 19 } , - \frac { 66 } { 19 } \right)$

Exam 3: Systems of Linear Equations and Inequalities

A plane flew 450 miles in 3 hours with the wind. It took 5 hours to travel the same distance against the wind. What is the rate of the plane in still air and the rate of the wind?

(Multiple Choice)

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Question 61

Graph the feasible region. x+y\leq3 and x\geq1,y\geq0

(Multiple Choice)

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Question 62

Graph the solution set of the compound inequality. $x + y < 3 \text { and } 4 x + y < 6$

(Multiple Choice)

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Question 63

Determine which point is the solution to the given system. y = 3x + 22 Y = 2x + 15

(Multiple Choice)

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Question 64

The graph of a system of linear equations is given. Identify whether the system is consistent or inconsistent. 2x-5y =4 4y =3x+1 $The graph of a system of linear equations is given. Identify whether the system is consistent or inconsistent. \begin{aligned} 2 x - 5 y & = 4 \\ 4 y & = 3 x + 1 \end{aligned}$

(Multiple Choice)

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Question 65

The perimeter of a triangle is 69 cm. The measure of the shortest side is 5 cm less than the middle side. The measure of the longest side is 5 cm less than the sum of the other two sides. Find the Lengths of the sides.

(Multiple Choice)

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Question 66

Solve the system by the addition method. x+y=- x+4y=-2.6

(Multiple Choice)

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Question 67

Determine which point is the solution to the given system. y=-x+32 y=x-11

(Multiple Choice)

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Question 68

Given the matrix M $\mathbf { M } = \left[ \begin{array} { c c | c } 1 & - 4 & 2 \\- 4 & - 3 & 5\end{array} \right]$ write the matrix obtained by multiplying the first row by 4 and then adding the first row to the second row.

(Multiple Choice)

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Question 69

Graph the solution set of the compound inequality. $4 x - 3 y \geq 60$ or $y > x$

(Multiple Choice)

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Question 70

Graph of the solution set of the inequality. $- x - 2 y \geq - 5$

(Multiple Choice)

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Question 71

Set up the augmented matrix. -4x+5y=-8 -8x+5y=2

(Multiple Choice)

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Question 72

Graph the solution set of the inequality. $\frac { x } { 3 } + \frac { y } { 4 } < 1$

(Multiple Choice)

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Question 73

Write a system of linear equations represented by the augmented matrix. $\left[ \begin{array} { c c | c } - 8 & 4 & - 9 \\ 2 & - 3 & - 5 \end{array} \right]$

(Multiple Choice)

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Question 74

Solve the system by using the Gauss-Jordan method. -5x+4y =-14 x-3y =16

(Multiple Choice)

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Question 75

A total of $4.80 consisting of dimes and quarters was collected from a soft drink vending machine. If there are 1 more quarters than dimes, find the number of dimes and the number of quarters.

(Multiple Choice)

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Question 76

The graph of a system of linear equations is given. Identify whether the system is dependent or independent. y =x+1 -2x+5y =5 $The graph of a system of linear equations is given. Identify whether the system is dependent or independent. \begin{aligned} y &=\frac{2}{5} x+1 \\ -2 x+5 y &=5 \end{aligned}$

(Multiple Choice)

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Question 77

A chemist wants to mix a 23% acid solution with a 43% acid solution to get 15 L of a 31% acid solution. How many liters of the 23% solution and how many liters of the 43% solution should be Mixed?

(Multiple Choice)

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Question 78

The graph of a system of linear equations is given. Identify the number of solutions to the system. 2x-5y =4 4y =3x+1 $The graph of a system of linear equations is given. Identify the number of solutions to the system. \begin{aligned} 2 x - 5 y & = 4 \\ 4 y & = 3 x + 1 \end{aligned}$

(Multiple Choice)

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Question 79

Graph the solution set of the inequality. $y \geq \frac { 3 } { 4 } x - 3$

(Multiple Choice)

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Question 80

Showing 61 - 80 of 118

A plane flew 450 miles in 3 hours with the wind. It took 5 hours to travel the same distance against the wind. What is the rate of the plane in still air and the rate of the wind?

Graph the feasible region. x+y\leq3 and x\geq1,y\geq0

Graph the solution set of the compound inequality. $x + y < 3 \text { and } 4 x + y < 6$

Determine which point is the solution to the given system. y = 3x + 22 Y = 2x + 15

The perimeter of a triangle is 69 cm. The measure of the shortest side is 5 cm less than the middle side. The measure of the longest side is 5 cm less than the sum of the other two sides. Find the Lengths of the sides.

Solve the system by the addition method. x+y=- x+4y=-2.6

Determine which point is the solution to the given system. y=-x+32 y=x-11

Given the matrix M $\mathbf { M } = \left[ \begin{array} { c c | c } 1 & - 4 & 2 \\- 4 & - 3 & 5\end{array} \right]$ write the matrix obtained by multiplying the first row by 4 and then adding the first row to the second row.

Graph the solution set of the compound inequality. $4 x - 3 y \geq 60$ or $y > x$

Graph of the solution set of the inequality. $- x - 2 y \geq - 5$

Set up the augmented matrix. -4x+5y=-8 -8x+5y=2

Graph the solution set of the inequality. $\frac { x } { 3 } + \frac { y } { 4 } < 1$

Write a system of linear equations represented by the augmented matrix. $\left[ \begin{array} { c c | c } - 8 & 4 & - 9 \\ 2 & - 3 & - 5 \end{array} \right]$

Solve the system by using the Gauss-Jordan method. -5x+4y =-14 x-3y =16

A total of $4.80 consisting of dimes and quarters was collected from a soft drink vending machine. If there are 1 more quarters than dimes, find the number of dimes and the number of quarters.

A chemist wants to mix a 23% acid solution with a 43% acid solution to get 15 L of a 31% acid solution. How many liters of the 23% solution and how many liters of the 43% solution should be Mixed?

The graph of a system of linear equations is given. Identify the number of solutions to the system. 2x-5y =4 4y =3x+1 $The graph of a system of linear equations is given. Identify the number of solutions to the system. \begin{aligned} 2 x - 5 y & = 4 \\ 4 y & = 3 x + 1 \end{aligned}$

Graph the solution set of the inequality. $y \geq \frac { 3 } { 4 } x - 3$

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables and Functions

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Rational Expressions and Rational Equations

Radicals and Complex Numbers

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Exam 3: Systems of Linear Equations and Inequalities

A plane flew 450 miles in 3 hours with the wind. It took 5 hours to travel the same distance against the wind. What is the rate of the plane in still air and the rate of the wind?

Graph the feasible region. x+y\leq3 and x\geq1,y\geq0

Graph the solution set of the compound inequality. x+y<3 and 4x+y<6x + y < 3 \text { and } 4 x + y < 6x+y<3 and 4x+y<6

Determine which point is the solution to the given system. y = 3x + 22 Y = 2x + 15

The graph of a system of linear equations is given. Identify whether the system is consistent or inconsistent. 2x-5y =4 4y =3x+1

The perimeter of a triangle is 69 cm. The measure of the shortest side is 5 cm less than the middle side. The measure of the longest side is 5 cm less than the sum of the other two sides. Find the Lengths of the sides.

Solve the system by the addition method. x+y=- x+4y=-2.6

Determine which point is the solution to the given system. y=-x+32 y=x-11

Given the matrix M M=[1−42−4−35]\mathbf { M } = \left[ \begin{array} { c c | c } 1 & - 4 & 2 \\- 4 & - 3 & 5\end{array} \right]M=[1−4​−4−3​25​] write the matrix obtained by multiplying the first row by 4 and then adding the first row to the second row.

Graph the solution set of the compound inequality. 4x−3y≥604 x - 3 y \geq 604x−3y≥60 or y>xy > xy>x

Graph of the solution set of the inequality. −x−2y≥−5- x - 2 y \geq - 5−x−2y≥−5

Set up the augmented matrix. -4x+5y=-8 -8x+5y=2

Graph the solution set of the inequality. x3+y4<1\frac { x } { 3 } + \frac { y } { 4 } < 13x​+4y​<1

Write a system of linear equations represented by the augmented matrix. [−84−92−3−5]\left[ \begin{array} { c c | c } - 8 & 4 & - 9 \\ 2 & - 3 & - 5 \end{array} \right][−82​4−3​−9−5​]

Solve the system by using the Gauss-Jordan method. -5x+4y =-14 x-3y =16

A total of $4.80 consisting of dimes and quarters was collected from a soft drink vending machine. If there are 1 more quarters than dimes, find the number of dimes and the number of quarters.

The graph of a system of linear equations is given. Identify whether the system is dependent or independent. y =x+1 -2x+5y =5

A chemist wants to mix a 23% acid solution with a 43% acid solution to get 15 L of a 31% acid solution. How many liters of the 23% solution and how many liters of the 43% solution should be Mixed?

The graph of a system of linear equations is given. Identify the number of solutions to the system. 2x-5y =4 4y =3x+1

Graph the solution set of the inequality. y≥34x−3y \geq \frac { 3 } { 4 } x - 3y≥43​x−3

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables and Functions

Polynomials

Rational Expressions and Rational Equations

Radicals and Complex Numbers

Quadratic Equations, Functions and Inequalities

Exponential and Logarithmic Functions and Applications

Conic Sections

Binomial Expansions, Sequences, and Series

Online: Transformations, Piecewise-Defined Functions, and Probability

Filters

Graph the solution set of the compound inequality. $x + y < 3 \text { and } 4 x + y < 6$

Given the matrix M $\mathbf { M } = \left[ \begin{array} { c c | c } 1 & - 4 & 2 \\- 4 & - 3 & 5\end{array} \right]$ write the matrix obtained by multiplying the first row by 4 and then adding the first row to the second row.

Graph the solution set of the compound inequality. $4 x - 3 y \geq 60$ or $y > x$

Graph of the solution set of the inequality. $- x - 2 y \geq - 5$

Graph the solution set of the inequality. $\frac { x } { 3 } + \frac { y } { 4 } < 1$

Write a system of linear equations represented by the augmented matrix. $\left[ \begin{array} { c c | c } - 8 & 4 & - 9 \\ 2 & - 3 & - 5 \end{array} \right]$

The graph of a system of linear equations is given. Identify the number of solutions to the system. 2x-5y =4 4y =3x+1 $The graph of a system of linear equations is given. Identify the number of solutions to the system. \begin{aligned} 2 x - 5 y & = 4 \\ 4 y & = 3 x + 1 \end{aligned}$

Graph the solution set of the inequality. $y \geq \frac { 3 } { 4 } x - 3$