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Q. 4

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Found in: Page 713

Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

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If a system of equations has one solution, the system is ________ and the equations are ________.

If a system of equations has one solution, the system is consistent and the equations are independent.

See the step by step solution

Step 1. Given information.

The given statement is:

If a system of equations has one solution, the system is ________ and the equations are ________.

Step 2. Determine the missing terms for the blanks.

Consistent and independent: A system of equations is consistent and independent if it has only one solution.

Consistent and dependent: A system of equations is consistent and dependent if it has an infinite number of solutions.

By using the above definitions, it is clear that the required words for the blanks are consistent and independent respectively.

Step 3. Conclusion.

If a system of equations has one solution, the system is consistent and the equations are independent.

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