Question

HELP!! When you solve a

system of equations
What are the three
possible outcomes ???

Answer 1

9514 1404 393

Answer:

• no solutions
• a finite number of solutions
• an infinite number of solutions

Explanation:

Your question is very general, including linear and non-linear equations of any number and/or degree. In the general case you're asking about, there will be ...

• no solutions -- no values of the variables satisfy all equations
• a finite number of solutions -- all equations are satisfied for some finite set of variable values
• an infinite number of solutions -- equations are dependent (or periodic*) so the set of solutions is an infinite set

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For 2 linear equations in 2 unknowns, there will be 0, 1, or infinite solutions.

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* Aperiodic equations may also have an infinite number of solutions. 1/sin(x)=0 is an example.