\begin{tabular}{l} Which ordered pair is the solution of the linear system \( 3 x+4 y=-10 \) and \( 2 x-4 y=0 \) ? \\ \begin{tabular}{|l|l|l}\hline A & \( (-6,2) \) \\ \hline B & \( (2,-6) \) \\ \hline 24 & C & \( (-2,-1) \) \\ \hline\end{tabular} \\ \hline\end{tabular} \begin{tabular}{|l|l}\hline D & \( (-1,-2) \) \\ \hline\end{tabular}

To find the solution of the linear system \( 3x + 4y = -10 \) and \( 2x - 4y = 0 \), we can substitute the pairs from the options into both equations. Let’s take option A: \( (-6, 2) \). 1. For \( 3x + 4y = -10 \): \( 3(-6) + 4(2) = -18 + 8 = -10 \) (True) 2. For \( 2x - 4y = 0 \): \( 2(-6) - 4(2) = -12 - 8 = -20 \) (False) Now let's check option B: \( (2, -6) \). 1. For \( 3x + 4y = -10 \): \( 3(2) + 4(-6) = 6 - 24 = -18 \) (False) 2. For \( 2x - 4y = 0 \): \( 2(2) - 4(-6) = 4 + 24 = 28 \) (False) Next, option C: \( (-2, -1) \). 1. For \( 3x + 4y = -10 \): \( 3(-2) + 4(-1) = -6 - 4 = -10 \) (True) 2. For \( 2x - 4y = 0 \): \( 2(-2) - 4(-1) = -4 + 4 = 0 \) (True) Lastly, option D: \( (-1, -2) \). 1. For \( 3x + 4y = -10 \): \( 3(-1) + 4(-2) = -3 - 8 = -11 \) (False) 2. For \( 2x - 4y = 0 \): \( 2(-1) - 4(-2) = -2 + 8 = 6 \) (False) The correct answer is option C: \( (-2, -1) \). Common mistakes when solving systems of equations include miscalculating when substituting values or neglecting to check both equations. Always plug the ordered pair into both equations to ensure it satisfies the entire system!