Solve the system of equations \( -6 x-4 y=10 \) and \( -5 x-2 y=-5 \) by combining the equations. \( \begin{array}{r}(-6 x-4 y=10) \\ (-5 x-2 y=-5) \\ -6 x-4 y=10 \\ -5 x-2 y=-5 \\ \hline 5 x+y=10\end{array} \)

Solve the system of equations \( -6x-4y=10;-5x-2y=-5 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}-6x-4y=10\\-5x-2y=-5\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}x=-\frac{5+2y}{3}\\-5x-2y=-5\end{array}\right.\) - step2: Substitute the value of \(x:\) \(-5\left(-\frac{5+2y}{3}\right)-2y=-5\) - step3: Multiply the terms: \(\frac{5\left(5+2y\right)}{3}-2y=-5\) - step4: Multiply both sides of the equation by LCD: \(\left(\frac{5\left(5+2y\right)}{3}-2y\right)\times 3=-5\times 3\) - step5: Simplify the equation: \(25+4y=-15\) - step6: Move the constant to the right side: \(4y=-15-25\) - step7: Subtract the numbers: \(4y=-40\) - step8: Divide both sides: \(\frac{4y}{4}=\frac{-40}{4}\) - step9: Divide the numbers: \(y=-10\) - step10: Substitute the value of \(y:\) \(x=-\frac{5+2\left(-10\right)}{3}\) - step11: Simplify: \(x=5\) - step12: Calculate: \(\left\{ \begin{array}{l}x=5\\y=-10\end{array}\right.\) - step13: Check the solution: \(\left\{ \begin{array}{l}x=5\\y=-10\end{array}\right.\) - step14: Rewrite: \(\left(x,y\right) = \left(5,-10\right)\) The solution to the system of equations \( -6x-4y=10 \) and \( -5x-2y=-5 \) is \( (x,y) = (5,-10) \).