8. Solve each system of equations using Clearly give the matrix and solution. U \( \left\{\begin{array}{l}10 x+12 y=6 \\ 7 x-3 y=-30\end{array}\right. \)

To solve the system of equations using matrices, we first represent the equations in matrix form \(Ax = b\). Here, the matrix \(A\) is: \[ \begin{pmatrix} 10 & 12 \\ 7 & -3 \end{pmatrix} \] The vector \(x\) is: \[ \begin{pmatrix} x \\ y \end{pmatrix} \] And the vector \(b\) is: \[ \begin{pmatrix} 6 \\ -30 \end{pmatrix} \] Next, we can use the inverse of matrix \(A\) (if it exists) to find \(x\) by computing \(x = A^{-1}b\). After calculating, we find the solution to be \(x = -6\) and \(y = 9\). To present the solution clearly: \[ \begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} -6 \\ 9 \end{pmatrix} \]