4. Dado el sistema, ¿cuál es el valor de \( \frac{x}{y} \) ? \( \begin{array}{l}2 x+3 y=16 \\ x-y=3\end{array} \) A) 0,4 B) 0,5 C) 2,5 D) 5,0

Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}2x+3y=16\\x-y=3\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}2x+3y=16\\x=3+y\end{array}\right.\) - step2: Substitute the value of \(x:\) \(2\left(3+y\right)+3y=16\) - step3: Simplify: \(6+5y=16\) - step4: Move the constant to the right side: \(5y=16-6\) - step5: Subtract the numbers: \(5y=10\) - step6: Divide both sides: \(\frac{5y}{5}=\frac{10}{5}\) - step7: Divide the numbers: \(y=2\) - step8: Substitute the value of \(y:\) \(x=3+2\) - step9: Calculate: \(x=5\) - step10: Calculate: \(\left\{ \begin{array}{l}x=5\\y=2\end{array}\right.\) - step11: Check the solution: \(\left\{ \begin{array}{l}x=5\\y=2\end{array}\right.\) - step12: Rewrite: \(\left(x,y\right) = \left(5,2\right)\) Para resolver el sistema de ecuaciones: \[ \begin{array}{l} 2x + 3y = 16 \\ x - y = 3 \end{array} \] hemos encontrado que la solución es \( (x, y) = (5, 2) \). Ahora, para encontrar el valor de \( \frac{x}{y} \): \[ \frac{x}{y} = \frac{5}{2} = 2.5 \] Por lo tanto, el valor de \( \frac{x}{y} \) es \( 2.5 \), lo que corresponde a la opción C) 2,5.