Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

In Problems 5–24, graph each equation of the system. Then solve the system to find the points of intersection.
$x^{2} + y^{2} = 4; y^{2} - x = 4$

The graph of the system of equations $x^{2} + y^{2} = 4; y^{2} - x = 4$ is:

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given

The system of non-linear equation:

$x^{2} + y^{2} = 4; y^{2} - x = 4$

To graph the equation and to find the point of intersection.

Step 2. Graph the equations

Graph the equations in the same plane.

Step 3. To find the point of intersection.

Substitute the second equation in the first equation,

${(y^{2} - 4)}^{2} + y^{2} = 4; y^{4} - 8 y^{2} + 16 + y^{2} = 4 y^{4} - 7 y^{2} + 12 = 0$

Step 4. Solve the equation

$y^{4} - 7 y^{2} + 12 = 0 (y^{2} - 4) (y^{2} - 3) = 0 y^{2} = 3, 4 y = \pm \sqrt{3}, \pm 2$

Step 5. Find x

When $y = \pm \sqrt{3}$ ,

$x^{2} + {(\pm \sqrt{3})}^{2} = 4 x^{2} + 3 = 4 x^{2} = 1 x = \pm 1$

When $y = \pm 2$ ,

$x^{2} + {(\pm 2)}^{2} = 4 x^{2} + 4 = 4 x^{2} = 0 x = 0$

The points of intersection are $(- 1, - \sqrt{3}) (- 1, \sqrt{3}), (0, - 2), (0, 2)$

Step 6. Plot the point of intersection

The graph of the system of non-linear equations with the point of intersection is:

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

In Problems 5–24, graph each equation of the system. Then solve the system to find the points of intersection.
$x^{2} + y^{2} = 4; y^{2} - x = 4$

Step by Step Solution

Step 1. Given

Step 2. Graph the equations

Step 3. To find the point of intersection.

Step 4. Solve the equation

Step 5. Find x

Step 6. Plot the point of intersection

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

In Problems 5–24, graph each equation of the system. Then solve the system to find the points of intersection.x2+y2=4; y2-x=4

Step by Step Solution

Step 1. Given

Step 2. Graph the equations

Step 3. To find the point of intersection.

Step 4. Solve the equation

Step 5. Find x

Step 6. Plot the point of intersection

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In Problems 5–24, graph each equation of the system. Then solve the system to find the points of intersection.
$x^{2} + y^{2} = 4; y^{2} - x = 4$