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Chapter 11: Q. 5 (page 772)

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

y=x2+1y=x+1

Short Answer

Expert verified

Solutions of system of equationsy=x2+1y=x+1 are (0,1)&(1,2)and the graph is

Step by step solution

01

Step 1. Given data

The given system of equations is

y=x2+1鈰�(i)y=x+1鈰�(ii)

02

Step 2. Graph of the system of equations

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

03

Step 3. Solution of system

subtract equation ii from equation i

y-y=(x2+1)-(x+1)0=x2-xx(x-1)=0

By zero product property

x=0

or

x-1=0x=1

So solutions are(0,1)&(1,2)

04

Step 4. Solution of system

Substitute x=0 in equation ii

role="math" localid="1646867196591" y=x+1y=0+1y=1

Substitute x=1in equation ii

role="math" y=x+1y=1+1y=2

So solutions of the system arerole="math" localid="1646867593062" (0,1)&(1,2)

05

Step 5. Verification

Substitutex=0&y=1in the system

1=02+11=0+1鈫�1=11=1

Substitute x=1&y=2in system

2=12+12=1+1鈫�2=22=2

The system of equations is satisfied by both solutions

so solutions (0,1)&(1,2)are correct

06

Step 6. Point of intersection

Locate the (0,1)&(1,2)for point of interception in the graph of a system of equations

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Most popular questions from this chapter

In Problems 23鈥�34, graph each system of linear inequalities by hand. Verify your results using a graphing utility:

2x+3y鈮�62x+3y鈮�0

Verify that the values of the variables listed are solutions of the system of equations.

3x-4y=412x-3y=-12x=2,y=12;2,12

Verify that the values of the variables listed are solutions of the system of equations.

x-y=3-3x+y=1x=-2,y=-5;-2,-5

In Problems 23鈥�34, graph each system of linear inequalities by hand. Verify your results using a graphing utility

2x+y鈮�-22x+y鈮�2

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

xy=1;y=2x+1
See all solutions

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