Chapter 4.1, Problem 81E

### 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

# How likely do you think it is that a “random” system of two equations in two unknowns has a unique solution? Give some justification for your answer.

To determine

The chance that a random system of two equations in two unknowns has a unique solution.

Explanation

Given Information:

A ārandomā system of two equations in two unknowns has a unique solution.

A system of two equations in two unknowns has a unique solution if two lines corresponding to the two equations intersect at a single point.

Since, the possibility that two lines in a plane intersect at a single point is very high.

For example, consider a system of two equations,

x+y=0 ā¦ā¦ (1)

And,

xāy=0 ā¦ā¦ (2)

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, x

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