I'm trying to solve these equations to solve a ciphertext which is encrypted by the Hill Cipher. I tried to solve these equations algebraically. (First choose two of them and try to eliminate one variable and after that choose another two and try the same thing for achieving two unknown two equations etc...)
\begin{align*} \tag{1}7a + 24b + 6c &= 1 \mod 26 \\ \tag{2}16a + 2b + 20c &= 0 \mod 26 \\ \tag{3}9a + 13b + 13c &= 10 \mod 26 \\ \tag{4}10a + 15b + 6c &= 17 \mod 26 \end{align*}
After this method I got $a = 17$, $b = 1$ and $c = 24$ and $a = 17$, $b = 1$, $c = 11$. However, it did not work with all of the four equations. Is there another way to solve these equations?