Find the solution of the system of equations. \[ \begin{aligned}-10 x-y & =-29 \\ 10 x+7 y & =23\end{aligned} \]

Solve the system of equations \( -10x-y=-29;10x+7y=23 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}-10x-y=-29\\10x+7y=23\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}y=29-10x\\10x+7y=23\end{array}\right.\) - step2: Substitute the value of \(y:\) \(10x+7\left(29-10x\right)=23\) - step3: Simplify: \(-60x+203=23\) - step4: Move the constant to the right side: \(-60x=23-203\) - step5: Subtract the numbers: \(-60x=-180\) - step6: Change the signs: \(60x=180\) - step7: Divide both sides: \(\frac{60x}{60}=\frac{180}{60}\) - step8: Divide the numbers: \(x=3\) - step9: Substitute the value of \(x:\) \(y=29-10\times 3\) - step10: Simplify: \(y=-1\) - step11: Calculate: \(\left\{ \begin{array}{l}x=3\\y=-1\end{array}\right.\) - step12: Check the solution: \(\left\{ \begin{array}{l}x=3\\y=-1\end{array}\right.\) - step13: Rewrite: \(\left(x,y\right) = \left(3,-1\right)\) La solución del sistema de ecuaciones es \( (x,y) = (3,-1) \).