To determine which statements are true about the ordered pair \((7, 19)\) and the given system of equations, we first must evaluate the ordered pair against each equation in the system. The system presented appears to be:
- \(2x - y = -5\)
- \(x + 3y = 22\)
Let's substitute \(x = 7\) and \(y = 19\) into each equation.
For the first equation:
\[ 2(7) - 19 = -5 \] \[ 14 - 19 = -5 \] \[ -5 = -5 \]
This statement is true, so \((7, 19)\) is a solution to the first equation.
For the second equation: \[ 7 + 3(19) = 22 \] \[ 7 + 57 = 22 \] \[ 64 \neq 22 \]
This statement is false, so \((7, 19)\) is not a solution to the second equation.
Given these evaluations, we can analyze the original statements:
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The ordered pair (7, 19) is a solution to the first equation because it makes the first equation true. - This is true.
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The ordered pair (7, 19) is a solution to the second equation because it makes the second equation true. - This is false.
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The ordered pair (7, 19) is not a solution to the system because it makes at least one of the equations false. - This is true.
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The ordered pair (7, 19) is a solution to the system because it makes both equations true. - This is false.
Final responses:
- The first statement is true.
- The second statement is false.
- The third statement is true.
- The fourth statement is false.