Question

Explain the three different types of solutions you can get when solving a system of equations.

Answer 1

Answer:

There are three possible outcomes for a system of linear equations: one unique solution, infinitely many solutions, and no solution.

Step-by-step explanation:

Answer 2

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Answer:

1. no solutions
2. a finite non-zero number of solutions
3. infinite solutions

Step-by-step explanation:

1. No Solutions

This case arises when the equations are inconsistent. No values of the variables can satisfy all of the equations. An example is ...

• y = x
• y = x+1

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2. Finite Number of Solutions

The number of distinct solutions depends on the degree of the system and the domain being considered. For example, an n-th degree polynomial equation in one variable will always have n solutions in the domain of complex numbers. However, it may or may not have any real-number solutions. (The question here has no context, so we have to assume it is about any system of equations of any degree or nature (rational, polynomial, exponential, mixed, or other.))

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3. Infinite solutions

An under-specified system, such as a system of 3 equations in 4 variables, may have an infinite number of solutions. In such a system, one or more of the variables may be allowed to assume any value. Systems that have dependent equations will fall into this category.