7) \( \begin{array}{l}-4 x+y=6 \\ -5 x-y=21\end{array} \)

To solve the system of equations, we can use the method of substitution or elimination. Here, let’s use the elimination method: First, we can express both equations: 1. \( y = 4x + 6 \) 2. \( y = -5x - 21 \) Now, we can set them equal to each other since they both equal \( y \): \( 4x + 6 = -5x - 21 \) Next, combine like terms: \( 4x + 5x = -21 - 6 \) \( 9x = -27 \) Dividing both sides by 9 gives: \( x = -3 \) Now substitute \( x \) back into one of the original equations to find \( y \): Using \( y = 4(-3) + 6 \): \( y = -12 + 6 = -6 \) So, the solution to the system is \( x = -3 \) and \( y = -6 \) or as a coordinate \((-3, -6)\). To verify, plug these values into the second equation: \( -5(-3) - (-6) = 15 + 6 = 21 \), which checks out! So the final answer is \( x = -3 \), \( y = -6 \).