Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

1st Edition

ISBN: 9780078682278

Author: McGraw-Hill, Berchie Holliday

Publisher: Glencoe/McGraw-Hill

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Question

Chapter 10.8, Problem 39E

To determine

To find: the solutions algebraically for the system of equations and then verify the answer by graphing each system.

Expert Solution & Answer

Answer to Problem 39E

(−3,4) and (4,−3)

Explanation of Solution

Given information:

x=−y+1..........(1)

xy=−12..........(2)

y2=25−x2..........(3)

Calculation:

Substitute x in equation (2) and solve y as follows:

(−y+1)y=−12 [Put x=−y+1]−y2+y=−12y2−y=12 [Divide each side by −1]y2−y−12=0 [Subtract 12 from each side]y=−(−1)±(−1)2−4(1)(−12)2(1) [Using −b±b2−4ac2a]=1±492=1±72y=4 or −3 ...(3)

Substitute the value of y in equation (1) and solve x as follows:

x=−(−3)+1 [For y=−3]=4x=−(4)+1 [For y=4]=−3

Thus, the point of intersection of equation (1) and (2) are (−3,4) and (4,−3) .

Substitute each value of y in equation (3) and solve x as shown below.

y2=25−x2x=±25−y2x=±25−(−3)2 [For y=−3]=±4x=±25−(4)2 [For y=4]=±3

The point of intersection of equation (3) and (2) are (−3,±4) and (4,±3) .

The common point of intersection in all the equations gives for the given system. Thus, the solutions are (−3,4) and (4,−3) .

Now use graphing calculator to plot equation (1) , (2) and (3) on same screen as shown below.

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 10.8, Problem 39E

The solution (x,y) obtained from the graph i.e. (−3,4) and (4,−3) which are same as the calculated solutions. Thus, the solutions are verified.

Chapter 10.8, Problem 38E

Chapter 10.8, Problem 40E

Chapter 10 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

Ch. 10.1 - Prob. 1CFU Ch. 10.1 - Prob. 2CFU Ch. 10.1 - Prob. 3CFU Ch. 10.1 - Prob. 4CFU Ch. 10.1 - Prob. 5CFU Ch. 10.1 - Prob. 6CFU Ch. 10.1 - Prob. 7CFU Ch. 10.1 - Prob. 8CFU Ch. 10.1 - Prob. 9CFU Ch. 10.1 - Prob. 10CFU

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