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True or false:
The inconsistent system has infinite number of solutions.
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Answer to Problem 3SGR
False. The system is said to be inconsistent when it has no solution.
Explanation of Solution
Given information:
The given statement is:
‘The inconsistent system has infinite number of 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.
The system with the infinite number of solutions is called as dependent system. When there is no solution for the given consistent system then it is said to be inconsistent system.
Therefore, the given statement is wrong. The corrected statement is:
‘The consistent system is said to be inconsistent system when it has no set of solutions.’
Chapter 6 Solutions
Algebra 1
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