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Chapter 5: Q. 69 (page 596)

In a system of linear equations, the two equations have the same slope. Describe the possible solutions to the system.

Short Answer

Expert verified

The possible solutions are:

1) Infinitely many solutions

2) No solution.

Step by step solution

01

Given 

In a system of linear equations, the two equations have the same slope.

02

To determine 

Describe the possible solutions to the system.

03

Calculation 

Case 1:If the y-intercepts are also the same:

Since the slopes are the same, they have the same slope and the same

y-intercept and so the lines are coincident.

A system of equations whose graphs are coincident lines has infinitely many solutions and is consistent and dependent.

Case 2: If the y-intercepts are not the same:

Since the slopes are the same and y-intercepts are different, the lines are parallel.

A system of equations whose graphs are parallel lines has no solution and is inconsistent and independent.

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