(2) \( 3 x+7 y=-9 \) 2) \( 5 x-2 y=26 \)

Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}3x+7y=-9\\5x-2y=26\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}x=-\frac{9+7y}{3}\\5x-2y=26\end{array}\right.\) - step2: Substitute the value of \(x:\) \(5\left(-\frac{9+7y}{3}\right)-2y=26\) - step3: Multiply the terms: \(-\frac{5\left(9+7y\right)}{3}-2y=26\) - step4: Multiply both sides of the equation by LCD: \(\left(-\frac{5\left(9+7y\right)}{3}-2y\right)\times 3=26\times 3\) - step5: Simplify the equation: \(-45-41y=78\) - step6: Move the constant to the right side: \(-41y=78+45\) - step7: Add the numbers: \(-41y=123\) - step8: Change the signs: \(41y=-123\) - step9: Divide both sides: \(\frac{41y}{41}=\frac{-123}{41}\) - step10: Divide the numbers: \(y=-3\) - step11: Substitute the value of \(y:\) \(x=-\frac{9+7\left(-3\right)}{3}\) - step12: Substitute back: \(x=\frac{-9+7\times 3}{3}\) - step13: Calculate: \(x=4\) - step14: Calculate: \(\left\{ \begin{array}{l}x=4\\y=-3\end{array}\right.\) - step15: Check the solution: \(\left\{ \begin{array}{l}x=4\\y=-3\end{array}\right.\) - step16: Rewrite: \(\left(x,y\right) = \left(4,-3\right)\) Para resolver el sistema de ecuaciones: 1) \( 3x + 7y = -9 \) 2) \( 5x - 2y = 26 \) Encontramos que la solución es: \[ (x, y) = (4, -3) \] Esto significa que \( x = 4 \) y \( y = -3 \).