Toanswer:Does a consistent and independent system of equations have an infinite number of solutions.
Answer to Problem 10SGR
A consistent and independent system of equations has finite number of solutions (one).
Explanation of Solution
Given information:
The given system of equations is consistent and independent.
If a system has at least one solution, then it is said to be consistent. If a consistent system of equations has exactly one solution, it is independent .
If a consistent system has an infinite number of solutions, it isdependent,when graphed such equations, represent the same line. If a system has no solution, it is said to be inconsistent .The graphs of such equations do not intersect, i.e., graphs are parallel. Consider system ofequations
The graph of both the equations is same, the solution of equation
Thus, a consistent and dependent system of equations has infinite number of solutions, and a consistent and independent system of equations has finite number of solutions (one).
Conclusion:
A consistent and independent system of equations has finite number of solutions (one).
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