The three equations are as you are using:
[tex]\begin{gathered} a+b+c=116 \\ 8a+4b+c=448 \\ 27a+9b+c=972 \end{gathered}[/tex]So by solving the system of linear equations:
[tex]\begin{bmatrix}{1} & {1} & {1} \\ {8} & {4} & {1} \\ {27} & {9} & {1}\end{bmatrix}\begin{bmatrix}{a} & {} & {} \\ {b} & {} & \\ {c} & & {}\end{bmatrix}=\begin{bmatrix}{116} & {} & {} \\ {448} & {} & \\ {972} & & {}\end{bmatrix}[/tex]Now i'm telling you to use transformation and then solve it. it'll be easy for you:
The first transformation is:
[tex]R_2-8R_1=R_2[/tex]Then:
[tex]R_3-27R_1=R_3_{}_{}[/tex]And then
[tex]R_3-\frac{9}{2}R_2=R_3[/tex]Then you'll get:
[tex]\begin{gathered} a+b+c=116 \\ -4b-7c=-480 \\ \frac{11}{2}c=0 \end{gathered}[/tex]