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Chapter 11: Q. 17 (page 772)

In Problems 5鈥�24, graph each equation of the system. Then solve the system to find the points of intersection.

x2+y2=4;y2-x=4

Short Answer

Expert verified

The graph of the system of equations x2+y2=4;y2-x=4is:

Step by step solution

01

Step 1. Given

The system of non-linear equation:

x2+y2=4;y2-x=4

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

02

Step 2. Graph the equations

Graph the equations in the same plane.

03

Step 3. To find the point of intersection.

Substitute the second equation in the first equation,

(y2-4)2+y2=4;y4-8y2+16+y2=4y4-7y2+12=0

04

Step 4. Solve the equation

y4-7y2+12=0(y2-4)(y2-3)=0y2=3,4y=卤3,卤2

05

Step 5. Find x

When y=卤3,

x2+(卤3)2=4x2+3=4x2=1x=卤1

When y=卤2,

x2+(卤2)2=4x2+4=4x2=0x=0

The points of intersection are (-1,-3)(-1,3),(0,-2),(0,2)

06

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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