Explanation:
The equations are given below as
[tex]\begin{gathered} 2a+b+c=2 \\ -a+b-c=-4 \\ a-2b+2c=6 \end{gathered}[/tex]
isolate a in equation (1) to give
[tex]a=\frac{2-b-c}{2}[/tex]
Susbtitute the equation of a in equation (2) and (3)
[tex]\begin{bmatrix}-\frac{2-b-c}{2}+b-c=-4\\ \frac{2-b-c}{2}-2b+2c=6\end{bmatrix}[/tex]
Simplifying the equation, we will have
[tex]\begin{bmatrix}\frac{3b-c-2}{2}=-4\\ \frac{-5b+3c+2}{2}=6\end{bmatrix}[/tex]
Isolate b from the equation below
[tex]\begin{gathered} \begin{equation*} \frac{3b-c-2}{2}=-4 \end{equation*} \\ b=\frac{c-6}{3} \end{gathered}[/tex]
substiuting , we will have
[tex]\begin{bmatrix}\frac{-5\cdot \frac{c-6}{3}+3c+2}{2}=6\end{bmatrix}[/tex]
On simplifying , we will have
[tex]\begin{gathered} \begin{bmatrix}\frac{2\left(c+9\right)}{3}=6\end{bmatrix} \\ 2c+18=18 \\ 2c=18-18 \\ 2c=0 \\ c=0 \end{gathered}[/tex][tex]\begin{gathered} b=\frac{c-6}{3} \\ b=\frac{0-6}{3} \\ b=-\frac{6}{3} \\ b=-2 \end{gathered}[/tex][tex]\begin{gathered} a=\frac{2-b-c}{2} \\ a=\frac{2-(-2)-0}{2} \\ a=\frac{2+2}{2} \\ a=\frac{4}{2} \\ a=2 \end{gathered}[/tex]
Hence,
The final answers are
[tex]a=2,b=-2,c=0[/tex]
The final answer is
