Chapter 4.1, Problem 69E

### Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Chapter
Section

### Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

# A system of three equations in two unknowns corresponds to three lines in the plane. Describe how these lines might be positioned if the system has a unique solution.

To determine

The position of three lines on a x-y plane if the system has a unique solution when the system of three equations in two unknowns corresponds to three lines in the plane.

Explanation

Given Information:

A system of three equations in two unknowns corresponds to three lines in the plane.

A system of three equations in two unknowns has a unique solution when,

1. The three lines in a plane corresponding to the three equations are distinct and not parallel and intersects at a unique point.

2. Two of the three lines are same and intersects with the third line at a unique point.

For Example,

Consider the equations,

x+y=0 ā¦ā¦ (1)

xāy=0 ā¦ā¦ (2)

x+2y=0 ā¦ā¦ (3)

To find the solution of the modified system of equations, graphically, plot the graphs of the equations and find the intersection point.

To plot the graph of the equations, find the ordered pairs of the equation.

Consider the equation, x+y=0

Substitute x=0 in the equation x+y=0

0+y=0y=0

Substitute x=5 in the equation x+y=0.

5+y=0y=ā5

Substitute x=ā4 in the equation x+y=0.

ā4+y=0y=4

Represent the values of x and y of the equation x+y=0 in a tabular form,

 x 0 5 ā4 y 0 ā5 4

Consider the equation, xāy=0

Substitute x=0 in the equation xāy=0

0āy=0āy=0y=0

Substitute x=3 in the equation xāy=0

3āy=0āy=ā3y=3

Substitute x=ā5 in the equation xāy

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