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

Solve the system of equations \( 10x+12y=6;7x-3y=-30 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}10x+12y=6\\7x-3y=-30\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}x=\frac{3-6y}{5}\\7x-3y=-30\end{array}\right.\) - step2: Substitute the value of \(x:\) \(7\times \frac{3-6y}{5}-3y=-30\) - step3: Simplify: \(\frac{7\left(3-6y\right)}{5}-3y=-30\) - step4: Multiply both sides of the equation by LCD: \(\left(\frac{7\left(3-6y\right)}{5}-3y\right)\times 5=-30\times 5\) - step5: Simplify the equation: \(21-57y=-150\) - step6: Move the constant to the right side: \(-57y=-150-21\) - step7: Subtract the numbers: \(-57y=-171\) - step8: Change the signs: \(57y=171\) - step9: Divide both sides: \(\frac{57y}{57}=\frac{171}{57}\) - step10: Divide the numbers: \(y=3\) - step11: Substitute the value of \(y:\) \(x=\frac{3-6\times 3}{5}\) - step12: Calculate: \(x=-3\) - step13: Calculate: \(\left\{ \begin{array}{l}x=-3\\y=3\end{array}\right.\) - step14: Check the solution: \(\left\{ \begin{array}{l}x=-3\\y=3\end{array}\right.\) - step15: Rewrite: \(\left(x,y\right) = \left(-3,3\right)\) The solution to the system of equations is \( (x, y) = (-3, 3) \).