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Q. 6

Precalculus Enhanced with Graphing Utilities
Found in: Page 772
Precalculus Enhanced with Graphing Utilities

Precalculus Enhanced with Graphing Utilities

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.

Solutions of system of equationsy=x2+1y=4x+1 are (0,1) & (4,17) and the graph is

See the step by step solution

Step by Step Solution

Step 1. Given data 

The given system of equations is

y=x2+1 (i)y=4x+1 (ii)

Step 2. Graph of the system of equations 

Plot the graph of y=x2+1 & y=4x+1on same cartesian plane

Step 3. Solution of system 

subtract equation ii from equation i


By zero product property




So x=0 & 4

Step 4. Solution of system 

Substitute x=0 in equation ii

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

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

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

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

Step 5. Verification 

Substitute x=0 &y=1in the system


Substitute x=4 & y=17 in system


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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