a) Answer The solution is ( x , y ) = ( 5 , 2 ) Explanation Given: The given equation is { x − 4 y = − 3 5 x − 6 y = 13 Calculation: Consider the following system of linear equations { x − 4 y = − 3............. ( 1 ) 5 x − 6 y = 13.............. ( 2 ) The two equations x − 4 y = − 3 and 5 x − 6 y = 13 are plotted below using MAPLE Multiply equation (1) by -5 and add the resultant to the equation (2) to get ( − 5 x + 20 y ) + ( 5 x = 6 y ) = 15 + 13 − 5 x + 20 y + 5 x − 6 y = 28 14 y = 28 y = 2 Put y = 2 in the equation (1) to get x − 4 ( 2 ) = − 3 x − 8 = − 3 x = − 3 + 8 = 5 Thus the solution is ( x , y ) = ( 5 , 2 ) The equation of the line at each step of the elimination process is the same. b) To determine To find: the graphs at the different steps. Answer The two equations 2 x − 3 y = 7 and − 4 x + 6 y = − 14 are equivalent. Explanation Given: The given equation is { 2 x − 3 y = 7 − 4 x + 6 y = − 14 Calculation: Consider the following system of linear equations { 2 x − 3 y = 7............. ( 3 ) − 4 x + 6 y = − 14............... ( 4 ) The two equations 2 x − 3 y = 7 and − 4 x + 6 y = − 14 are plotted below using MAPLE Multiply equation (3) by -2 to get − 4 x + 6 y = − 14 Note that this is same as the equation (4) also the graph of both the equations coincide. Thus, the two equations 2 x − 3 y = 7 and − 4 x + 6 y = − 14 are equivalent. Hence the system of equations has infinite number of solutions.

3rd Edition

ISBN: 9781285607160

Author: Larson

Publisher: CENGAGE CO

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Question

Chapter 7, Problem 5PS

To determine

To find: the graphs at the different steps.

Expert Solution

Answer to Problem 5PS

The solution is (x,y)=(5,2)

Explanation of Solution

Given:

The given equation is

{x−4y=−35x−6y=13

Calculation:

Consider the following system of linear equations

{x−4y=−3.............(1)5x−6y=13..............(2)

The two equations x−4y=−3 and 5x−6y=13 are plotted below using MAPLE

EBK PRECALCULUS W/LIMITS, Chapter 7, Problem 5PS , additional homework tip 1

Multiply equation (1) by -5 and add the resultant to the equation (2) to get

(−5x+20y)+(5x=6y)=15+13−5x+20y+5x−6y=2814y=28y=2

Put y=2 in the equation (1) to get

x−4(2)=−3x−8=−3x=−3+8=5

Thus the solution is (x,y)=(5,2)

The equation of the line at each step of the elimination process is the same.

To determine

To find: the graphs at the different steps.

Expert Solution

Answer to Problem 5PS

The two equations 2x−3y=7 and −4x+6y=−14 are equivalent.

Explanation of Solution

Given:

The given equation is

{2x−3y=7−4x+6y=−14

Calculation:

Consider the following system of linear equations

{2x−3y=7.............(3)−4x+6y=−14...............(4)

The two equations 2x−3y=7 and −4x+6y=−14 are plotted below using MAPLE

EBK PRECALCULUS W/LIMITS, Chapter 7, Problem 5PS , additional homework tip 2

Multiply equation (3) by -2 to get

−4x+6y=−14

Note that this is same as the equation (4) also the graph of both the equations coincide.

Thus, the two equations 2x−3y=7 and −4x+6y=−14 are equivalent.

Hence the system of equations has infinite number of solutions.

Chapter 7, Problem 4PS

Chapter 7, Problem 6PS

Chapter 7 Solutions

EBK PRECALCULUS W/LIMITS

Ch. 7.1 - Prob. 1E Ch. 7.1 - Prob. 2E Ch. 7.1 - Prob. 3E Ch. 7.1 - Prob. 4E Ch. 7.1 - Prob. 5E Ch. 7.1 - Prob. 6E Ch. 7.1 - Prob. 7E Ch. 7.1 - Prob. 8E Ch. 7.1 - Prob. 9E Ch. 7.1 - Prob. 10E

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