6 vilai \( x+y+z \) jika diketahui \( 2 x+y-3 z=3 \) \( -y+5 z=-2 ; 2 x+2 y-z=-1 \) adalah \( \ldots \) -4 -3 -2

Solve the system of equations \( 2x+y-3z=3;-y+5z=-2;2x+2y-z=-1 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}2x+y-3z=3\\-y+5z=-2\\2x+2y-z=-1\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}y=3-2x+3z\\-y+5z=-2\\2x+2y-z=-1\end{array}\right.\) - step2: Substitute the value of \(y:\) \(\left\{ \begin{array}{l}-\left(3-2x+3z\right)+5z=-2\\2x+2\left(3-2x+3z\right)-z=-1\end{array}\right.\) - step3: Simplify: \(\left\{ \begin{array}{l}-3+2x+2z=-2\\-2x+6+5z=-1\end{array}\right.\) - step4: Solve the equation: \(\left\{ \begin{array}{l}x=\frac{1-2z}{2}\\-2x+6+5z=-1\end{array}\right.\) - step5: Substitute the value of \(x:\) \(-2\times \frac{1-2z}{2}+6+5z=-1\) - step6: Simplify: \(5+7z=-1\) - step7: Move the constant to the right side: \(7z=-1-5\) - step8: Subtract the numbers: \(7z=-6\) - step9: Divide both sides: \(\frac{7z}{7}=\frac{-6}{7}\) - step10: Divide the numbers: \(z=-\frac{6}{7}\) - step11: Substitute the value of \(z:\) \(x=\frac{1-2\left(-\frac{6}{7}\right)}{2}\) - step12: Simplify: \(x=\frac{19}{14}\) - step13: Substitute the values of \(x,z:\) \(y=3-2\times \frac{19}{14}+3\left(-\frac{6}{7}\right)\) - step14: Simplify: \(y=-\frac{16}{7}\) - step15: Calculate: \(\left\{ \begin{array}{l}x=\frac{19}{14}\\y=-\frac{16}{7}\\z=-\frac{6}{7}\end{array}\right.\) - step16: Check the solution: \(\left\{ \begin{array}{l}x=\frac{19}{14}\\y=-\frac{16}{7}\\z=-\frac{6}{7}\end{array}\right.\) - step17: Rewrite: \(\left(x,y,z\right) = \left(\frac{19}{14},-\frac{16}{7},-\frac{6}{7}\right)\) Untuk sistem persamaan yang diberikan, solusinya adalah: \( x = \frac{19}{14} \) \( y = -\frac{16}{7} \) \( z = -\frac{6}{7} \) Jadi, nilai \( x+y+z \) adalah \( \frac{19}{14} - \frac{16}{7} - \frac{6}{7} \). Kita dapat menghitung nilai ini dengan menggabungkan denominator yang sama: \( \frac{19}{14} - \frac{16}{7} - \frac{6}{7} = \frac{19}{14} - \frac{16+6}{7} = \frac{19}{14} - \frac{22}{7} \) Kita dapat mengubah denominator yang sama dengan mengalikan dengan 14: \( \frac{19}{14} - \frac{22}{7} = \frac{19}{14} - \frac{22 \times 2}{7 \times 2} = \frac{19}{14} - \frac{44}{14} \) Kita dapat menggabungkan denominator yang sama: \( \frac{19}{14} - \frac{44}{14} = \frac{19-44}{14} = \frac{-25}{14} \) Jadi, nilai \( x+y+z \) adalah \( -\frac{25}{14} \) atau \( -1\frac{11}{14} \).