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Chapter 11: Q. 9 (page 772)

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

y=x;y=2-x

Short Answer

Expert verified

The graph of the system of equations y=x;y=2-xis:

Step by step solution

01

Step 1. Given

The system of non-linear equation:

y=x;y=2-x

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.

Equate both the equations,

x=2-x

Squaring on both sides, we get,

x=(2-x)2x=4-4x+x2x2-5x+4=0

04

Step 4. Solve the equation

x2-5x+4=0x2-4x-x+4=0(x-1)(x-4)=0x=1,4

05

Step 5. Find y

When x=1,

y=2-xy=2-1=1

When x=4,

y=2-(4)=-2

The points of intersection are (1,1),(4,-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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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

x+4y鈮�8x+4y鈮�4

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

Graph each inequality by hand.

x2+y2鈮�9

If a system of equations has one solution, the system is ________ and the equations are ________.

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

x2+y2=4;y=x2-9
See all solutions

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