a) \( \left\{\begin{array}{c}2 x+5 y=16 \\ x+3 y=6\end{array}\right. \)

Solve the system of equations \( 2x+5y=16;x+3y=6 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}2x+5y=16\\x+3y=6\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}2x+5y=16\\x=6-3y\end{array}\right.\) - step2: Substitute the value of \(x:\) \(2\left(6-3y\right)+5y=16\) - step3: Simplify: \(12-y=16\) - step4: Move the constant to the right side: \(-y=16-12\) - step5: Subtract the numbers: \(-y=4\) - step6: Change the signs: \(y=-4\) - step7: Substitute the value of \(y:\) \(x=6-3\left(-4\right)\) - step8: Simplify: \(x=18\) - step9: Calculate: \(\left\{ \begin{array}{l}x=18\\y=-4\end{array}\right.\) - step10: Check the solution: \(\left\{ \begin{array}{l}x=18\\y=-4\end{array}\right.\) - step11: Rewrite: \(\left(x,y\right) = \left(18,-4\right)\) La solución de las ecuaciones dadas es \( (x,y) = (18,-4) \).