To determine which statements are true about the ordered pair (2, 3) and the system of equations, we need to substitute \( x = 2 \) and \( y = 3 \) into both equations:
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The first equation is \( 3x + 4y = 18 \). Substituting in the values: \[ 3(2) + 4(3) = 6 + 12 = 18 \] This is true.
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The second equation is \( 2x - 2y = 2 \). Substituting in the values: \[ 2(2) - 2(3) = 4 - 6 = -2 \] This is false.
Based on this analysis, we can evaluate the statements:
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The ordered pair (2, 3) is not a solution to the system of linear equations.
- True (because it does not satisfy both equations)
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When (2, 3) is substituted into the second equation, the equation is false.
- True (the second equation does not hold)
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When (2, 3) is substituted into the first equation, the equation is false.
- False (the first equation holds true)
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When (2, 3) is substituted into the second equation, the equation is true.
- False (the second equation does not hold)
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The ordered pair (2, 3) is a solution to the system of linear equations.
- False (it does not satisfy both equations)
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When (2, 3) is substituted into the first equation, the equation is true.
- True (the first equation is satisfied)
Therefore, the true statements are:
- The ordered pair (2, 3) is not a solution to the system of linear equations.
- When (2, 3) is substituted into the second equation, the equation is false.
- When (2, 3) is substituted into the first equation, the equation is true.
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