To determine the truth of the statements regarding the ordered pair (2, 3) and the system of equations given by:
- \(3x + 4y = 18\)
- \(2x - 2y = 2\)
we will substitute \(x = 2\) and \(y = 3\) into each equation.
First equation:
\[ 3(2) + 4(3) = 18 \] \[ 6 + 12 = 18 \] \[ 18 = 18 \quad \text{(True)} \]
Second equation:
\[ 2(2) - 2(3) = 2 \] \[ 4 - 6 = 2 \] \[ -2 = 2 \quad \text{(False)} \]
Summary of evaluations:
- The ordered pair \((2, 3)\) is a solution to the first equation.
- The ordered pair \((2, 3)\) is not a solution to the second equation.
- Therefore, \((2, 3)\) is not a solution to the system of equations as it does not satisfy both equations.
Final Responses:
- True: The ordered pair (2, 3) is a solution to the system of linear equations. (False)
- True: When (2, 3) is substituted into the second equation, the equation is false. (True)
- True: When (2, 3) is substituted into the first equation, the equation is true. (True)
- True: The ordered pair (2, 3) is not a solution to the system of linear equations. (True)
Therefore, the valid statements are:
- 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.
- The ordered pair (2, 3) is not a solution to the system of linear equations.
1 answer