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Which statements are true about the ordered pair (10, 5) and the system of equations? {2x−5y=−5x+2y=11 Select each correct answer. Responses The ordered pair (10, 5) is a solution to the first equation because it makes the first equation true. The ordered pair , begin ordered pair 10 comma 5 end ordered pair, is a solution to the first equation because it makes the first equation true. The ordered pair (10, 5) is a solution to the second equation because it makes the second equation true. The ordered pair , begin ordered pair 10 comma 5 end ordered pair, is a solution to the second equation because it makes the second equation true. The ordered pair (10, 5) is not a solution to the system because it makes at least one of the equations false. The ordered pair , begin ordered pair 10 comma 5 end ordered pair, is not a solution to the system because it makes at least one of the equations false. The ordered pair (10, 5) is a solution to the system because it makes both equations true. The ordered pair , begin ordered pair 10 comma 5 end ordered pair, is a solution to the system because it makes both equations true.

User BCDeWitt
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Final answer:

The ordered pair (10, 5) is not a solution to either equation in the given system. Substituting the values into the equations shows that the pair does not satisfy either equation, making it not a solution to the system. The correct answer is option: c) The ordered pair (10, 5) is not a solution to the system because it makes at least one of the equations false. The ordered pair , begin ordered pair 10 comma 5 end ordered pair, is not a solution to the system because it makes at least one of the equations false.

Step-by-step explanation:

To determine whether the ordered pair (10, 5) is a solution to the system of equations, we must substitute x with 10 and y with 5 into each equation and see if the equations hold true.

  • First equation: 2x - 5y = 0
    Substitute (10, 5): 2(10) - 5(5) = 20 - 25 = -5
    The equation does not hold true; therefore, the ordered pair (10, 5) is not a solution to the first equation.
  • Second equation: -5x + 2y = 11
    Substitute (10, 5): -5(10) + 2(5) = -50 + 10 = -40
    The equation does not hold true; thus, the ordered pair (10, 5) is not a solution to the second equation.

Since the ordered pair does not solve either equation, it cannot be a solution to the system. The statement that (10, 5) is not a solution to the system because it makes at least one of the equations false is, in fact, true.

User London Student
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