To determine which statements are true about the ordered pair (10, 5) in relation to the system of equations:
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First, let's write down the system of equations clearly:
- \( 2x - 5y = -5 \)
- \( x + 2y = 11 \)
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Now substitute (10, 5) into each equation:
For the first equation: \[ 2(10) - 5(5) = -5 \] This simplifies to: \[ 20 - 25 = -5 \] \[ -5 = -5 \quad \text{(True)} \]
For the second equation: \[ 10 + 2(5) = 11 \] This simplifies to: \[ 10 + 10 = 11 \] \[ 20 = 11 \quad \text{(False)} \]
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Now evaluate the statements:
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The ordered pair (10, 5) is a solution to the first equation because it makes the first equation true. (True)
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The ordered pair (10, 5) is a solution to the second equation because it makes the second equation true. (False)
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The ordered pair (10, 5) is not a solution to the system because it makes at least one of the equations false. (True)
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The ordered pair (10, 5) is a solution to the system because it makes both equations true. (False)
Final Answers:
- The ordered pair (10, 5) is a solution to the first equation because it makes the first equation true.
- The ordered pair (10, 5) is not a solution to the system because it makes at least one of the equations false.
1 answer