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7th Edition

Stefan Waner + 1 other

Publisher: Cengage Learning

ISBN: 9781337280426

Chapter 3.1, Problem 69E

Textbook Problem

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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.

**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,

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,

Substitute

Substitute

Substitute

Represent the values of *x* and *y* of the equation

x |
|||

y |

Consider the equation,

Substitute

Substitute

Substitute

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