\( 2 x-4 y=10 \) and \( 3 x+5 y=-29 \)

Solve the system of equations \( 2x-4y=10;3x+5y=-29 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}2x-4y=10\\3x+5y=-29\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}x=5+2y\\3x+5y=-29\end{array}\right.\) - step2: Substitute the value of \(x:\) \(3\left(5+2y\right)+5y=-29\) - step3: Simplify: \(15+11y=-29\) - step4: Move the constant to the right side: \(11y=-29-15\) - step5: Subtract the numbers: \(11y=-44\) - step6: Divide both sides: \(\frac{11y}{11}=\frac{-44}{11}\) - step7: Divide the numbers: \(y=-4\) - step8: Substitute the value of \(y:\) \(x=5+2\left(-4\right)\) - step9: Calculate: \(x=-3\) - step10: Calculate: \(\left\{ \begin{array}{l}x=-3\\y=-4\end{array}\right.\) - step11: Check the solution: \(\left\{ \begin{array}{l}x=-3\\y=-4\end{array}\right.\) - step12: Rewrite: \(\left(x,y\right) = \left(-3,-4\right)\) The solution to the system of equations \(2x-4y=10\) and \(3x+5y=-29\) is \(x=-3\) and \(y=-4\).