Solve the following system of equations. State whether the system is consistent and independent, consistent and dependent, or inconsistent.

Question

Solve the following system of equations. State whether the system is consistent and independent, consistent and dependent, or inconsistent. -4x+7y=28 4x-7y=32

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Alaia 3 weeks 2021-09-08T12:26:36+00:00 1 Answer 0

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    2021-09-08T12:27:55+00:00

    Answer:

    Inconsistent

    Step-by-step explanation:

    If a system has at least one solution, it is said to be consistent.

    If a consistent system has exactly one solution, it is independent.

    If a consistent system has an infinite number of solutions, it is dependent.

    A system of equations is called an inconsistent system of equations if there is no solution.

    Given the system of two equations

    \left\{\begin{array}{l}-4x+7y=28\\ \\4x-7y=32\end{array}\right.

    Add these two equations:

    (-4x+7y)+(4x-7y)=28+32\\ \\-4x+7y+4x-7y=60\\ \\(-4x+4x)+(7y-7y)=60\\ \\0=60

    This is false statement, hence, the system of two equations has no solution and is inconsistent.

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