True or false:
The consistent system is said to be independent system when it has exactly two solutions.
Answer to Problem 2SGR
False. The consistent system is said to be independent system when it has exactly one set of solutions.
Explanation of Solution
Given information:
The given statement is:
‘The consistent system is said to be independent system when it has exactly two solutions.’
A system of two linear equations can have the following three solution conditions:
- One solution
- An infinite number of solutions
- No solution.
That’s why the systems of equations are classified by the set of solutions to satisfy the equations.
Know that:
If the system of two equations contains has least one solution then it is said to be consistent. Like this, the consistent system is said to be independent when it contain at least one solution.
Therefore, the given statement is false. The corrected statement is:
‘The consistent system is said to be independent system when it has exactly one set of solutions.’
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