Q. 4 - Precalculus Enhanced with Graphing Utilities

Question

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

Step-by-Step Solution

Answer

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

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.