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Chapter 11: Q. 7 (page 772)

Graph each equation of the system. Then solve the system to find the points of intersection.

y=36-x2y=8-x

Short Answer

Expert verified

Solutions of system of equationsy=36-x2y=8-xare (4+2,4-2)&(4-2,4+2)and the graph is

Step by step solution

01

Step 1. Given data  

The given system of equations is

y=36-x2鈰�(i)y=8-x鈰�(ii)

02

Step 2. Graph of the system of equations  

Plot the graph of y=36-x2&y=8-xon same cartesian plane

03

Step 3. Solution of system  

Equate both equations

36-x2=8-x36-x2=8-x236-x2=x2-16x+642x2-16x+28=0

use quadratic formula

x=-b卤b2-4ac2ax=-(-16)卤(-16)2-4(2)(28)2(2)x=16卤324x=4卤2

04

Step 4. Solution of system  

Substitute x=4+2in equation ii

y=8-xy=8-4+2y=4-2

Substitutex=4-2 in equation ii

y=8-xy=8-4-2y=4+2

So solutions of the system are(4+2,4-2)&(4-2,4+2)

05

Step 6. Point of intersection 

Locate (4+2,4-2)&(4-2,4+2)for point of interception in the graph of a system of equations

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Most popular questions from this chapter

Graph the equation:y=3x+2

Solve each system of equations. If the system has no solution, say that it is inconsistent.

4x+5y=-3-2y=-8

The sum of two numbers is the same as their product, and the difference of their reciprocals is 3. Find the numbers.

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

y=3x-5;x2+y2=5

In Problems, use the division algorithm to rewrite each improper fraction as the sum of a quotient and proper fraction. Find the partial fraction decomposition of the proper fraction. Finally, express the improper fraction as the sum of a quotient and the partial fraction decomposition.

x4-5x2+x-4x2+4x+4
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