AP CALCULUS TEST PREP-WORKBOOK

6th Edition

ISBN: 9781418300258

Author: Demana

Publisher: SAVVAS L

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Question

Chapter 0.1, Problem 54E

(a)

To determine

To find: Solve the equations simultaneously by an algebraic method, either substitution or elimination. Write the conclusion.

(a)

Expert Solution

Answer to Problem 54E

The system has no solution.it is an inconsistent system.

Explanation of Solution

Given information:

The given system of equation is 2x−5y=3, 6x−15y=9 .This system of equation is dependent and inconsistent.

Concept used: Elimination method to find the solution of system is used.

Calculation:

The given equations are:

2x−5y=3 ...(1)6x−15y=9....2

Multiply equation (1) by 3 it gives:

6x−15y=9.....(3)

Now subtract equation 2 from (3)

6x−6x+15y−15y=9−9 0+0=0 0=0

Elimination gives an equation that is always true The two equation in the system represents the same line. This is a dependent system that has infinite solutions.

Now check the condition of inconsistency that is if there is a system of equation

a1x+b1y=ca2x+b2y=c

Then the system is consistent and represent same line if:

a1a2=b1b2=c1c2

Check this condition with the given system of equation it gives:

26=−5−15=3913=13=13

The system of equation satisfies the above condition of consistency hence the system is dependent and has infinite many solutions.

(b)

To determine

To find: The solution of the equation of system by graph.

(b)

Expert Solution

Answer to Problem 54E

The system is consistent

Explanation of Solution

Given information:

The given system of equation is 2x−5y=3,6x−15y=9 .This system of equation is dependent and inconsistent.

Calculation:

To draw the graph of the equation 2x−5y=3,6x−15y=9 . Substitute different values of x to find the corresponding values of y .

The graph of the above equation is given below.

AP CALCULUS TEST PREP-WORKBOOK, Chapter 0.1, Problem 54E

As it is clear from the graph that two lines are coincide hence there is infinite number of solution of this system of equation has no solution.

Chapter 0.1, Problem 53E

Chapter 0.1, Problem 55E

Chapter 0 Solutions

AP CALCULUS TEST PREP-WORKBOOK

Ch. 0.1 - Prob. 1QR Ch. 0.1 - Prob. 2QR Ch. 0.1 - Prob. 3QR Ch. 0.1 - Prob. 4QR Ch. 0.1 - Prob. 5QR Ch. 0.1 - Prob. 6QR Ch. 0.1 - Prob. 7QR Ch. 0.1 - Prob. 8QR Ch. 0.1 - Prob. 9QR Ch. 0.1 - Prob. 10QR

Ch. 0.1 - Prob. 1E Ch. 0.1 - Prob. 2E Ch. 0.1 - Prob. 3E Ch. 0.1 - Prob. 4E Ch. 0.1 - Prob. 5E Ch. 0.1 - Prob. 6E Ch. 0.1 - Prob. 7E Ch. 0.1 - Prob. 8E Ch. 0.1 - Prob. 9E Ch. 0.1 - Prob. 10E Ch. 0.1 - Prob. 11E Ch. 0.1 - Prob. 12E Ch. 0.1 - Prob. 13E Ch. 0.1 - Prob. 14E Ch. 0.1 - Prob. 15E Ch. 0.1 - Prob. 16E Ch. 0.1 - Prob. 17E Ch. 0.1 - Prob. 18E Ch. 0.1 - Prob. 19E Ch. 0.1 - Prob. 20E Ch. 0.1 - Prob. 21E Ch. 0.1 - Prob. 22E Ch. 0.1 - Prob. 23E Ch. 0.1 - Prob. 24E Ch. 0.1 - Prob. 25E Ch. 0.1 - Prob. 26E Ch. 0.1 - Prob. 27E Ch. 0.1 - Prob. 28E Ch. 0.1 - Prob. 29E Ch. 0.1 - Prob. 30E Ch. 0.1 - Prob. 31E Ch. 0.1 - Prob. 32E Ch. 0.1 - Prob. 33E Ch. 0.1 - Prob. 34E Ch. 0.1 - Prob. 35E Ch. 0.1 - Prob. 36E Ch. 0.1 - Prob. 37E Ch. 0.1 - Prob. 38E Ch. 0.1 - Prob. 39E Ch. 0.1 - Prob. 40E Ch. 0.1 - Prob. 41E Ch. 0.1 - Prob. 42E Ch. 0.1 - Prob. 43E Ch. 0.1 - Prob. 44E Ch. 0.1 - Prob. 45E Ch. 0.1 - Prob. 46E Ch. 0.1 - Prob. 47E Ch. 0.1 - Prob. 48E Ch. 0.1 - Prob. 49E Ch. 0.1 - Prob. 50E Ch. 0.1 - Prob. 51E Ch. 0.1 - Prob. 52E Ch. 0.1 - Prob. 53E Ch. 0.1 - Prob. 54E Ch. 0.1 - Prob. 55E Ch. 0.1 - Prob. 56E Ch. 0.1 - Prob. 57E Ch. 0.1 - Prob. 58E Ch. 0.2 - Prob. 1QR Ch. 0.2 - Prob. 2QR Ch. 0.2 - Prob. 3QR Ch. 0.2 - Prob. 4QR Ch. 0.2 - Prob. 5QR Ch. 0.2 - Prob. 6QR Ch. 0.2 - Prob. 7QR Ch. 0.2 - Prob. 8QR Ch. 0.2 - Prob. 9QR Ch. 0.2 - Prob. 10QR Ch. 0.2 - Prob. 11QR Ch. 0.2 - Prob. 12QR Ch. 0.2 - Prob. 1E Ch. 0.2 - Prob. 2E Ch. 0.2 - Prob. 3E Ch. 0.2 - Prob. 4E Ch. 0.2 - Prob. 5E Ch. 0.2 - Prob. 6E Ch. 0.2 - Prob. 7E Ch. 0.2 - Prob. 8E Ch. 0.2 - Prob. 9E Ch. 0.2 - Prob. 10E Ch. 0.2 - Prob. 11E Ch. 0.2 - Prob. 12E Ch. 0.2 - Prob. 13E Ch. 0.2 - Prob. 14E Ch. 0.2 - Prob. 15E Ch. 0.2 - Prob. 16E Ch. 0.2 - Prob. 17E Ch. 0.2 - Prob. 18E Ch. 0.2 - Prob. 19E Ch. 0.2 - Prob. 20E Ch. 0.2 - Prob. 21E Ch. 0.2 - Prob. 22E Ch. 0.2 - Prob. 23E Ch. 0.2 - Prob. 24E Ch. 0.2 - Prob. 25E Ch. 0.2 - Prob. 26E Ch. 0.2 - Prob. 27E Ch. 0.2 - Prob. 28E Ch. 0.2 - Prob. 29E Ch. 0.2 - Prob. 30E Ch. 0.2 - Prob. 31E Ch. 0.2 - Prob. 32E Ch. 0.2 - Prob. 33E Ch. 0.2 - Prob. 34E Ch. 0.2 - Prob. 35E Ch. 0.2 - Prob. 36E Ch. 0.2 - Prob. 37E Ch. 0.2 - Prob. 38E Ch. 0.2 - Prob. 39E Ch. 0.2 - Prob. 40E Ch. 0.2 - Prob. 41E Ch. 0.2 - Prob. 42E Ch. 0.2 - Prob. 43E Ch. 0.2 - Prob. 44E Ch. 0.2 - Prob. 45E Ch. 0.2 - Prob. 46E Ch. 0.2 - Prob. 47E Ch. 0.2 - Prob. 48E Ch. 0.2 - Prob. 49E Ch. 0.2 - Prob. 50E Ch. 0.2 - Prob. 51E Ch. 0.2 - Prob. 52E Ch. 0.2 - Prob. 53E Ch. 0.2 - Prob. 54E Ch. 0.2 - Prob. 55E Ch. 0.2 - Prob. 56E Ch. 0.2 - Prob. 57E Ch. 0.2 - Prob. 58E Ch. 0.2 - Prob. 59E Ch. 0.2 - Prob. 60E Ch. 0.2 - Prob. 61E Ch. 0.2 - Prob. 62E Ch. 0.2 - Prob. 63E Ch. 0.2 - Prob. 64E Ch. 0.2 - Prob. 65E Ch. 0.2 - Prob. 66E Ch. 0.2 - Prob. 67E Ch. 0.2 - Prob. 68E Ch. 0.2 - Prob. 69E Ch. 0.2 - Prob. 70E Ch. 0.2 - Prob. 71E Ch. 0.2 - Prob. 72E Ch. 0.3 - Prob. 1QR Ch. 0.3 - Prob. 2QR Ch. 0.3 - Prob. 3QR Ch. 0.3 - Prob. 4QR Ch. 0.3 - Prob. 5QR Ch. 0.3 - Prob. 6QR Ch. 0.3 - Prob. 7QR Ch. 0.3 - Prob. 8QR Ch. 0.3 - Prob. 9QR Ch. 0.3 - Prob. 10QR Ch. 0.3 - Prob. 1E Ch. 0.3 - Prob. 2E Ch. 0.3 - Prob. 3E Ch. 0.3 - Prob. 4E Ch. 0.3 - Prob. 5E Ch. 0.3 - Prob. 6E Ch. 0.3 - Prob. 7E Ch. 0.3 - Prob. 8E Ch. 0.3 - Prob. 9E Ch. 0.3 - Prob. 10E Ch. 0.3 - Prob. 11E Ch. 0.3 - Prob. 12E Ch. 0.3 - Prob. 13E Ch. 0.3 - Prob. 14E Ch. 0.3 - Prob. 15E Ch. 0.3 - Prob. 16E Ch. 0.3 - Prob. 17E Ch. 0.3 - Prob. 18E Ch. 0.3 - Prob. 19E Ch. 0.3 - Prob. 20E Ch. 0.3 - Prob. 21E Ch. 0.3 - Prob. 22E Ch. 0.3 - Prob. 23E Ch. 0.3 - Prob. 24E Ch. 0.3 - Prob. 25E Ch. 0.3 - Prob. 26E Ch. 0.3 - Prob. 27E Ch. 0.3 - Prob. 28E Ch. 0.3 - Prob. 29E Ch. 0.3 - Prob. 30E Ch. 0.3 - Prob. 31E Ch. 0.3 - Prob. 32E Ch. 0.3 - Prob. 33E Ch. 0.3 - Prob. 34E Ch. 0.3 - Prob. 35E Ch. 0.3 - Prob. 36E Ch. 0.3 - Prob. 37E Ch. 0.3 - Prob. 38E Ch. 0.3 - Prob. 39E Ch. 0.3 - Prob. 40E Ch. 0.3 - Prob. 41E Ch. 0.3 - Prob. 42E Ch. 0.3 - Prob. 43E Ch. 0.3 - Prob. 44E Ch. 0.3 - Prob. 45E Ch. 0.3 - Prob. 46E Ch. 0.3 - Prob. 47E Ch. 0.3 - Prob. 48E Ch. 0.3 - Prob. 49E Ch. 0.3 - Prob. 1QQ Ch. 0.3 - Prob. 2QQ Ch. 0.3 - Prob. 3QQ Ch. 0.3 - Prob. 4QQ Ch. 0.4 - Prob. 1QR Ch. 0.4 - Prob. 2QR Ch. 0.4 - Prob. 3QR Ch. 0.4 - Prob. 4QR Ch. 0.4 - Prob. 5QR Ch. 0.4 - Prob. 6QR Ch. 0.4 - Prob. 7QR Ch. 0.4 - Prob. 8QR Ch. 0.4 - Prob. 9QR Ch. 0.4 - Prob. 10QR Ch. 0.4 - Prob. 1E Ch. 0.4 - Prob. 2E Ch. 0.4 - Prob. 3E Ch. 0.4 - Prob. 4E Ch. 0.4 - Prob. 5E Ch. 0.4 - Prob. 6E Ch. 0.4 - Prob. 7E Ch. 0.4 - Prob. 8E Ch. 0.4 - Prob. 9E Ch. 0.4 - Prob. 10E Ch. 0.4 - Prob. 11E Ch. 0.4 - Prob. 12E Ch. 0.4 - Prob. 13E Ch. 0.4 - Prob. 14E Ch. 0.4 - Prob. 15E Ch. 0.4 - Prob. 16E Ch. 0.4 - Prob. 17E Ch. 0.4 - Prob. 18E Ch. 0.4 - Prob. 19E Ch. 0.4 - Prob. 20E Ch. 0.4 - Prob. 21E Ch. 0.4 - Prob. 22E Ch. 0.4 - Prob. 23E Ch. 0.4 - Prob. 24E Ch. 0.4 - Prob. 25E Ch. 0.4 - Prob. 26E Ch. 0.4 - Prob. 27E Ch. 0.4 - Prob. 28E Ch. 0.4 - Prob. 29E Ch. 0.4 - Prob. 30E Ch. 0.4 - Prob. 31E Ch. 0.4 - Prob. 32E Ch. 0.4 - Prob. 33E Ch. 0.4 - Prob. 34E Ch. 0.4 - Prob. 35E Ch. 0.4 - Prob. 36E Ch. 0.4 - Prob. 37E Ch. 0.4 - Prob. 38E Ch. 0.4 - Prob. 39E Ch. 0.4 - Prob. 40E Ch. 0.4 - Prob. 41E Ch. 0.4 - Prob. 42E Ch. 0.4 - Prob. 43E Ch. 0.4 - Prob. 44E Ch. 0.4 - Prob. 45E Ch. 0.4 - Prob. 46E Ch. 0.4 - Prob. 47E Ch. 0.4 - Prob. 48E Ch. 0.5 - Prob. 1QR Ch. 0.5 - Prob. 2QR Ch. 0.5 - Prob. 3QR Ch. 0.5 - Prob. 4QR Ch. 0.5 - Prob. 5QR Ch. 0.5 - Prob. 6QR Ch. 0.5 - Prob. 7QR Ch. 0.5 - Prob. 8QR Ch. 0.5 - Prob. 9QR Ch. 0.5 - Prob. 10QR Ch. 0.5 - Prob. 1E Ch. 0.5 - Prob. 2E Ch. 0.5 - Prob. 3E Ch. 0.5 - Prob. 4E Ch. 0.5 - Prob. 5E Ch. 0.5 - Prob. 6E Ch. 0.5 - Prob. 7E Ch. 0.5 - Prob. 8E Ch. 0.5 - Prob. 9E Ch. 0.5 - Prob. 10E Ch. 0.5 - Prob. 11E Ch. 0.5 - Prob. 12E Ch. 0.5 - Prob. 13E Ch. 0.5 - Prob. 14E Ch. 0.5 - Prob. 15E Ch. 0.5 - Prob. 16E Ch. 0.5 - Prob. 17E Ch. 0.5 - Prob. 18E Ch. 0.5 - Prob. 19E Ch. 0.5 - Prob. 20E Ch. 0.5 - Prob. 21E Ch. 0.5 - Prob. 22E Ch. 0.5 - Prob. 23E Ch. 0.5 - Prob. 24E Ch. 0.5 - Prob. 25E Ch. 0.5 - Prob. 26E Ch. 0.5 - Prob. 27E Ch. 0.5 - Prob. 28E Ch. 0.5 - Prob. 29E Ch. 0.5 - Prob. 30E Ch. 0.5 - Prob. 31E Ch. 0.5 - Prob. 32E Ch. 0.5 - Prob. 33E Ch. 0.5 - Prob. 34E Ch. 0.5 - Prob. 35E Ch. 0.5 - Prob. 36E Ch. 0.5 - Prob. 37E Ch. 0.5 - Prob. 38E Ch. 0.5 - Prob. 39E Ch. 0.5 - Prob. 40E Ch. 0.5 - Prob. 41E Ch. 0.5 - Prob. 42E Ch. 0.5 - Prob. 43E Ch. 0.5 - Prob. 44E Ch. 0.5 - Prob. 45E Ch. 0.5 - Prob. 46E Ch. 0.5 - Prob. 47E Ch. 0.5 - Prob. 48E Ch. 0.5 - Prob. 49E Ch. 0.5 - Prob. 50E Ch. 0.5 - Prob. 51E Ch. 0.5 - Prob. 52E Ch. 0.5 - Prob. 53E Ch. 0.5 - Prob. 54E Ch. 0.5 - Prob. 55E Ch. 0.5 - Prob. 56E Ch. 0.5 - Prob. 57E Ch. 0.5 - Prob. 58E Ch. 0.5 - Prob. 59E Ch. 0.5 - Prob. 60E Ch. 0.5 - Prob. 61E Ch. 0.5 - Prob. 62E Ch. 0.6 - Prob. 1QR Ch. 0.6 - Prob. 2QR Ch. 0.6 - Prob. 3QR Ch. 0.6 - Prob. 4QR Ch. 0.6 - Prob. 5QR Ch. 0.6 - Prob. 6QR Ch. 0.6 - Prob. 7QR Ch. 0.6 - Prob. 8QR Ch. 0.6 - Prob. 9QR Ch. 0.6 - Prob. 10QR Ch. 0.6 - Prob. 1E Ch. 0.6 - Prob. 2E Ch. 0.6 - Prob. 3E Ch. 0.6 - Prob. 4E Ch. 0.6 - Prob. 5E Ch. 0.6 - Prob. 6E Ch. 0.6 - Prob. 7E Ch. 0.6 - Prob. 8E Ch. 0.6 - Prob. 9E Ch. 0.6 - Prob. 10E Ch. 0.6 - Prob. 11E Ch. 0.6 - Prob. 12E Ch. 0.6 - Prob. 13E Ch. 0.6 - Prob. 14E Ch. 0.6 - Prob. 15E Ch. 0.6 - Prob. 16E Ch. 0.6 - Prob. 17E Ch. 0.6 - Prob. 18E Ch. 0.6 - Prob. 19E Ch. 0.6 - Prob. 20E Ch. 0.6 - Prob. 21E Ch. 0.6 - Prob. 22E Ch. 0.6 - Prob. 23E Ch. 0.6 - Prob. 24E Ch. 0.6 - Prob. 25E Ch. 0.6 - Prob. 26E Ch. 0.6 - Prob. 27E Ch. 0.6 - Prob. 28E Ch. 0.6 - Prob. 29E Ch. 0.6 - Prob. 30E Ch. 0.6 - Prob. 31E Ch. 0.6 - Prob. 32E Ch. 0.6 - Prob. 33E Ch. 0.6 - Prob. 34E Ch. 0.6 - Prob. 35E Ch. 0.6 - Prob. 36E Ch. 0.6 - Prob. 37E Ch. 0.6 - Prob. 38E Ch. 0.6 - Prob. 39E Ch. 0.6 - Prob. 40E Ch. 0.6 - Prob. 41E Ch. 0.6 - Prob. 42E Ch. 0.6 - Prob. 43E Ch. 0.6 - Prob. 44E Ch. 0.6 - Prob. 45E Ch. 0.6 - Prob. 46E Ch. 0.6 - Prob. 47E Ch. 0.6 - Prob. 48E Ch. 0.6 - Prob. 49E Ch. 0.6 - Prob. 50E Ch. 0.6 - Prob. 51E Ch. 0.6 - Prob. 52E Ch. 0.6 - Prob. 53E Ch. 0.6 - Prob. 54E Ch. 0.6 - Prob. 55E Ch. 0.6 - Prob. 56E Ch. 0.6 - Prob. 57E Ch. 0.6 - Prob. 58E Ch. 0.6 - Prob. 59E Ch. 0.6 - Prob. 60E Ch. 0.6 - Prob. 61E Ch. 0.6 - Prob. 62E Ch. 0.6 - Prob. 1QQ Ch. 0.6 - Prob. 2QQ Ch. 0.6 - Prob. 3QQ Ch. 0.6 - Prob. 4QQ Ch. 0 - Prob. 1RWDT Ch. 0 - Prob. 2RWDT Ch. 0 - Prob. 3RWDT Ch. 0 - Prob. 4RWDT Ch. 0 - Prob. 5RWDT Ch. 0 - Prob. 6RWDT Ch. 0 - Prob. 7RWDT Ch. 0 - Prob. 8RWDT Ch. 0 - Prob. 9RWDT Ch. 0 - Prob. 10RWDT Ch. 0 - Prob. 1RE Ch. 0 - Prob. 2RE Ch. 0 - Prob. 3RE Ch. 0 - Prob. 4RE Ch. 0 - Prob. 5RE Ch. 0 - Prob. 6RE Ch. 0 - Prob. 7RE Ch. 0 - Prob. 8RE Ch. 0 - Prob. 9RE Ch. 0 - Prob. 10RE Ch. 0 - Prob. 11RE Ch. 0 - Prob. 12RE Ch. 0 - Prob. 13RE Ch. 0 - Prob. 14RE Ch. 0 - Prob. 15RE Ch. 0 - Prob. 16RE Ch. 0 - Prob. 17RE Ch. 0 - Prob. 18RE Ch. 0 - Prob. 19RE Ch. 0 - Prob. 20RE Ch. 0 - Prob. 21RE Ch. 0 - Prob. 22RE Ch. 0 - Prob. 23RE Ch. 0 - Prob. 24RE Ch. 0 - Prob. 25RE Ch. 0 - Prob. 26RE Ch. 0 - Prob. 27RE Ch. 0 - Prob. 28RE Ch. 0 - Prob. 29RE Ch. 0 - Prob. 30RE Ch. 0 - Prob. 31RE Ch. 0 - Prob. 32RE Ch. 0 - Prob. 33RE Ch. 0 - Prob. 34RE Ch. 0 - Prob. 35RE Ch. 0 - Prob. 36RE Ch. 0 - Prob. 37RE Ch. 0 - Prob. 38RE Ch. 0 - Prob. 39RE Ch. 0 - Prob. 40RE Ch. 0 - Prob. 41RE Ch. 0 - Prob. 42RE Ch. 0 - Prob. 43RE Ch. 0 - Prob. 44RE Ch. 0 - Prob. 45RE Ch. 0 - Prob. 46RE Ch. 0 - Prob. 47RE Ch. 0 - Prob. 48RE Ch. 0 - Prob. 49RE Ch. 0 - Prob. 50RE Ch. 0 - Prob. 51RE Ch. 0 - Prob. 52RE Ch. 0 - Prob. 53RE Ch. 0 - Prob. 54RE Ch. 0 - Prob. 55RE Ch. 0 - Prob. 56RE Ch. 0 - Prob. 57RE Ch. 0 - Prob. 58RE Ch. 0 - Prob. 59RE Ch. 0 - Prob. 60RE Ch. 0 - Prob. 61RE Ch. 0 - Prob. 62RE Ch. 0 - Prob. 63RE Ch. 0 - Prob. 64RE Ch. 0 - Prob. 65RE Ch. 0 - Prob. 66RE Ch. 0 - Prob. 67RE Ch. 0 - Prob. 68EP Ch. 0 - Prob. 69EP Ch. 0 - Prob. 70EP

Knowledge Booster

Solve the equations simultaneously by an algebraic method, either substitution or elimination. Write the conclusion.

Solution Summary: The author explains that the system of equations is dependent and inconsistent. Elimination gives an equation that is always true.

To find: Solve the equations simultaneously by an algebraic method, either substitution or elimination. Write the conclusion.

Answer to Problem 54E

Explanation of Solution

To find: The solution of the equation of system by graph.

Answer to Problem 54E

Explanation of Solution

Chapter 0 Solutions