Chapter 4.1, Problem 77E

### 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

# Select one: If the addition or subtraction of two linear equations results in the equation 0 = 3 , then the graphs of those equations are(A) equal(B) parallel(C) perpendicular(D) not parallel.

To determine

The correct option for the statement, “If the addition or subtraction of two linear equations results in the equation 0=3, then the graphs of those equations are” from the provided options.

Explanation

Given Information:

The provided options are,

(A) Equal

(B) Parallel

(C) Perpendicular

(D) Not parallel

Consider the statement, āIf the addition or subtraction of two linear equations results in the equation 0=3, then the graphs of those equations areā.

The condition 0=3 happens when the system of linear equations has no solution.

Therefore, the lines corresponding to the equations does not intersect.

To find out the correct option, letās take an example as,

For example:

Consider the equations,

2x+2y=3 ā¦ā¦ (1)

ā2xā2y=0 ā¦ā¦ (2)

Add the equations (1) and (2),

Ā Ā Ā Ā 2x+2y=3Ā ā2xā2y=0_Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā 0=3

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

Consider the equation, 2x+2y=3

Substitute x=0 in the equation 2x+2y=3,

2(0)+2y=32y=3y=32

Substitute x=3 in the equation 2x+2y=3,

2(3)+2y=36+2y=32y=3ā6y=ā32

Substitute x=ā5 in the equation 2x+2y=3,

2(ā5)+2y=3ā10+2y=32y=13y=132

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