Question: For each ordered pair, determine whether it is a solution to the system of equations. \[…

For each ordered pair, determine whether it is a solution to the system of equations.

\[ \begin{cases} y = -3x - 4 \\ 9x + 2y = -5 \end{cases} \]

Is it a solution?

\[ \begin{array}{c|c|c} (x, y) & \text{Yes} & \text{No} \\ \hline (0, -4) & \circ & \circ \\ (-3, 11) & \circ & \circ \\ (2, 6) & \circ & \circ \\ (1, -7) & \circ & \circ \end{array} \]

Solution

The system of equations given is: \[ \begin{cases} y = -3x - 4 & \\ 9x + 2y = -5 & \end{cases} \] We will check each ordered pair to determine if it is a solution to the system. 1. Ordered Pair (0, -4): Substitute \(x = 0\) and \(y = -4\) into the first equation: \[ -4 = -3(0) - 4 \] \[ -4 = -4 \quad \text{(True)} \] Substitute \(x = 0\) and \(y = -4\) into the second equation: \[ 9(0) + 2(-4) = -5 \] \[ -8 = -5 \quad \text{(False)} \] So, \((0, -4)\) is not a solution. 2. Ordered Pair (-3, 11): Substitute \(x = -3\) and \(y = 11\) into the first equation: \[ 11 = -3(-3) - 4 \] \[ 11 = 9 - 4 \] \[ 11 = 5 \quad \text{(False)} \] So, \((-3, 11)\) is not a solution. 3. Ordered Pair (2, 6): Substitute \(x = 2\) and \(y = 6\) into the first equation: \[ 6 = -3(2) - 4 \] \[ 6 = -6 - 4 \] \[ 6 = -10 \quad \text{(False)} \] So, \((2, 6)\) is not a solution. 4. Ordered Pair (1, -7): Substitute \(x = 1\) and \(y = -7\) into the first equation: \[ -7 = -3(1) - 4 \] \[ -7 = -3 - 4 \] \[ -7 = -7 \quad \text{(True)} \] Substitute \(x = 1\) and \(y = -7\) into the second equation: \[ 9(1) + 2(-7) = -5 \] \[ 9 - 14 = -5 \] \[ -5 = -5 \quad \text{(True)} \] So, \((1, -7)\) is a solution. Conclusion: - (0, -4): No - (-3, 11): No - (2, 6): No - (1, -7): Yes