\( \left\{\begin{array}{l}3 x-8 y=-19 \\ 5 x+16 y=27\end{array}\right. \) (У відповіді запиши значення виразу \( (x+y)) \)

Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}3x-8y=-19\\5x+16y=27\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}x=\frac{-19+8y}{3}\\5x+16y=27\end{array}\right.\) - step2: Substitute the value of \(x:\) \(5\times \frac{-19+8y}{3}+16y=27\) - step3: Simplify: \(\frac{5\left(-19+8y\right)}{3}+16y=27\) - step4: Multiply both sides of the equation by LCD: \(\left(\frac{5\left(-19+8y\right)}{3}+16y\right)\times 3=27\times 3\) - step5: Simplify the equation: \(-95+88y=81\) - step6: Move the constant to the right side: \(88y=81+95\) - step7: Add the numbers: \(88y=176\) - step8: Divide both sides: \(\frac{88y}{88}=\frac{176}{88}\) - step9: Divide the numbers: \(y=2\) - step10: Substitute the value of \(y:\) \(x=\frac{-19+8\times 2}{3}\) - step11: Calculate: \(x=-1\) - step12: Calculate: \(\left\{ \begin{array}{l}x=-1\\y=2\end{array}\right.\) - step13: Check the solution: \(\left\{ \begin{array}{l}x=-1\\y=2\end{array}\right.\) - step14: Rewrite: \(\left(x,y\right) = \left(-1,2\right)\) Решив систему уравнений, мы получили значения \( x = -1 \) и \( y = 2 \). Теперь найдем значение выражения \( x + y \): \[ x + y = -1 + 2 = 1 \] Таким образом, значение выражения \( (x+y) \) равно \( 1 \).