Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

Graph each equation of the system. Then solve the system to find the points of intersection.
$\{\begin{cases} y = x^{2} + 1 \\ y = 4 x + 1 \end{cases}$

Solutions of system of equations $\{\begin{cases} y = x^{2} + 1 \\ y = 4 x + 1 \end{cases}$ are $(0, 1) & (4, 17)$ and the graph is

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given data

The given system of equations is

$\{\begin{cases} y = x^{2} + 1 \dots (i) \\ y = 4 x + 1 \dots (i i) \end{cases}$

Step 2. Graph of the system of equations

Plot the graph of $y = x^{2} + 1 & y = 4 x + 1$ on same cartesian plane

Step 3. Solution of system

subtract equation ii from equation i

$y - y = (x^{2} + 1) - (4 x + 1) 0 = x^{2} - 4 x 0 = x (x - 4)$

By zero product property

$x - 4 = 0 x = 4$

$x = 0$

So $x = 0 & 4$

Step 4. Solution of system

Substitute $x = 0$ in equation ii

role="math" localid="1646869492730" $y = 4 x + 1 y = 4 (0) + 1 y = 1$

Substituterole="math" localid="1646869479187" $x = 4$ in equation ii

role="math" localid="1646869502982" $y = 4 x + 1 y = 4 (4) + 1 y = 17$

So solutions of the system are role="math" localid="1646869524607" $(0, 1) & (4, 17)$

Step 5. Verification

Substitute $x = 0 & y = 1$ in the system

$\{\begin{cases} 1 = 0^{2} + 1 \\ 1 = 4 (0) + 1 \end{cases} \to \{\begin{cases} 1 = 1 \\ 1 = 1 \end{cases}$

Substitute $x = 4 & y = 17$ in system

$\{\begin{cases} 17 = {(4)}^{2} + 1 \\ 17 = 4 (4) + 1 \end{cases} \to \{\begin{cases} 17 = 17 \\ 17 = 17 \end{cases}$

The system of equations is satisfied by both solutions

so solutions $(0, 1) & (4, 17)$ are correct

Step 6. Point of intersection

Locate the $(0, 1) & (4, 17)$ for point of interception in the graph of a system of equations

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

Graph each equation of the system. Then solve the system to find the points of intersection.
$\{\begin{cases} y = x^{2} + 1 \\ y = 4 x + 1 \end{cases}$

Step by Step Solution

Step 1. Given data

Step 2. Graph of the system of equations

Step 3. Solution of system

Step 4. Solution of system

Step 5. Verification

Step 6. Point of intersection

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

Graph each equation of the system. Then solve the system to find the points of intersection.y=x2+1y=4x+1

Step by Step Solution

Step 1. Given data

Step 2. Graph of the system of equations

Step 3. Solution of system

Step 4. Solution of system

Step 5. Verification

Step 6. Point of intersection

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Graph each equation of the system. Then solve the system to find the points of intersection.
$\{\begin{cases} y = x^{2} + 1 \\ y = 4 x + 1 \end{cases}$