8. \( \left\{\begin{array}{l}-5 x+15 y=-35 \\ -3 y-2 x=-14\end{array}\right. \)

Solve the system of equations \( -5x+15y=-35;-3y-2x=-14 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}-5x+15y=-35\\-3y-2x=-14\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}x=7+3y\\-3y-2x=-14\end{array}\right.\) - step2: Substitute the value of \(x:\) \(-3y-2\left(7+3y\right)=-14\) - step3: Simplify: \(-9y-14=-14\) - step4: Move the constant to the right side: \(-9y=-14+14\) - step5: Add the numbers: \(-9y=0\) - step6: Change the signs: \(9y=0\) - step7: Rewrite the expression: \(y=0\) - step8: Substitute the value of \(y:\) \(x=7+3\times 0\) - step9: Substitute back: \(x=7\) - step10: Calculate: \(\left\{ \begin{array}{l}x=7\\y=0\end{array}\right.\) - step11: Check the solution: \(\left\{ \begin{array}{l}x=7\\y=0\end{array}\right.\) - step12: Rewrite: \(\left(x,y\right) = \left(7,0\right)\) The solution to the system of equations is \( (x, y) = (7, 0) \).