8. \( \begin{aligned} 6 x-3 y & =-3 \\ -5 x+6 y & =41\end{aligned} \)

To solve the system of equations, you can use substitution or elimination. Let's use the elimination method here. First, we can rearrange the first equation \(6x - 3y = -3\) into a more convenient form: 1. \(2x - y = -1\) (Divide the entire equation by 3) Next, we can express \(y\) in terms of \(x\): 2. \(y = 2x + 1\) Now, substitute this expression for \(y\) into the second equation: \(-5x + 6(2x + 1) = 41\) Distributing gives: \(-5x + 12x + 6 = 41\) Combine like terms: \(7x + 6 = 41\) Now, solve for \(x\): \(7x = 41 - 6\) \(7x = 35\) \(x = 5\) Now, substitute \(x\) back into the expression for \(y\): \(y = 2(5) + 1 = 11\) Thus, the solution to the system of equations is \(x = 5\) and \(y = 11\). To double-check, you can plug \( (5, 11) \) back into both original equations to ensure they hold true. Always a good practice!