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Define a consistent and independent system of equations. How many solutions does it have?

Mathematics

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  1. Answer Question 1.

    A system of equations with the same number of unknowns where its equations are consistent with each other and independent is called a consistent and independent system. This type of system has exactly one unique solution.

    Answer: consistent and independent

  2. Answer Question 2.

    An ordered pair of numbers that is a solution to both equations in a system is called a solution to a system of equations.

    Answer: solution

  3. Answer Question 3 by referring to the graph.

    The graph shows that the two lines intersect at the point (2,1)(2, 1).

    Answer: (2,1)\boxed{(2, 1)}

  4. Answer Question 4.

    If the lines in a system of equations coincide, they are the same line, meaning every point on the line is a solution. Therefore, the system has infinitely many solutions and is said to be consistent and dependent.

    Answer: infinitely many, consistent and dependent

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