Questions: QUESTION 10 If the systems of linear equations has many (infinte) solutions, then it is considered a. Decay, Decrease b. Inconsistent c. Graphing, Substitution, and Elimination d. Consistent, Independent e. Growth, Increase f. Consistent, Dependent

QUESTION 10
If the systems of linear equations has many (infinte) solutions, then it is considered
a. Decay, Decrease
b. Inconsistent
c. Graphing, Substitution, and Elimination
d. Consistent, Independent
e. Growth, Increase
f. Consistent, Dependent

Transcript text: QUESTION 10 If the systems of linear equations has many (infinte) solutions, then it is considered a. Decay, Decrease b. Inconsistent c. Graphing, Substitution, and Elimination d. Consistent, Independent e. Growth, Increase f. Consistent, Dependent

Solution

Solution Steps

To determine the nature of a system of linear equations, we need to analyze the number of solutions it has. A system with infinitely many solutions is considered "consistent and dependent." This means the equations describe the same line or plane, leading to overlapping solutions.

Step 1: Understanding the Nature of the System

A system of linear equations can have three types of solutions: no solution, exactly one solution, or infinitely many solutions. When a system has infinitely many solutions, it means that the equations are dependent, and they describe the same line or plane in a geometric sense.

Step 2: Classifying the System

For a system with infinitely many solutions, it is classified as "consistent and dependent." This classification indicates that the equations are not independent and overlap completely, leading to an infinite number of solutions.