Select the correct answer. What is the value of \( a \) in this linear system? \( \begin{array}{l}a-b+c=-6 \\ b-c=5 \\ 2 a-2 c=4 \\ \text { A. } 1 \\ \text { B. }-3 \\ \text { C. } 2 \\ \text { D. }-1\end{array} \)

Solve the system of equations \( a-b+c=-6;b-c=5;2a-2c=4 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}a-b+c=-6\\b-c=5\\2a-2c=4\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}a=-6+b-c\\b-c=5\\2a-2c=4\end{array}\right.\) - step2: Substitute the value of \(a:\) \(\left\{ \begin{array}{l}b-c=5\\2\left(-6+b-c\right)-2c=4\end{array}\right.\) - step3: Simplify: \(\left\{ \begin{array}{l}b-c=5\\-12+2b-4c=4\end{array}\right.\) - step4: Solve the equation: \(\left\{ \begin{array}{l}b=5+c\\-12+2b-4c=4\end{array}\right.\) - step5: Substitute the value of \(b:\) \(-12+2\left(5+c\right)-4c=4\) - step6: Simplify: \(-2-2c=4\) - step7: Move the constant to the right side: \(-2c=4+2\) - step8: Add the numbers: \(-2c=6\) - step9: Change the signs: \(2c=-6\) - step10: Divide both sides: \(\frac{2c}{2}=\frac{-6}{2}\) - step11: Divide the numbers: \(c=-3\) - step12: Substitute the value of \(c:\) \(b=5-3\) - step13: Simplify: \(b=2\) - step14: Substitute the values of \(b,c:\) \(a=-6+2-\left(-3\right)\) - step15: Simplify: \(a=-1\) - step16: Calculate: \(\left\{ \begin{array}{l}a=-1\\b=2\\c=-3\end{array}\right.\) - step17: Check the solution: \(\left\{ \begin{array}{l}a=-1\\b=2\\c=-3\end{array}\right.\) - step18: Rewrite: \(\left(a,b,c\right) = \left(-1,2,-3\right)\) The solution to the system of equations is \( a = -1 \), \( b = 2 \), and \( c = -3 \). Therefore, the value of \( a \) in this linear system is \( -1 \), which corresponds to option D.