Step 1: Convert all decimals to fractions

$$\begin{array}{ cccc }~~ x&+~~9~ y&+~~7~ z&~=~1243\\7~ x&+~~5~ y&+~~~~ z&~=~715\\4~ x&+~~7~ y&+~~4~ z&~=~979\end{array}$$

Step 2: Multiply the first equation by $ -7 $ and add the result to the second equation. The result is:

$$\begin{array}{ cccc }~~ x&+~~9~ y&+~~7~ z&~=~1243\\&-~~~58~ y&-~~~48~ z&~=~-7986\\4~ x&+~~7~ y&+~~4~ z&~=~979\end{array}$$

Step 3: Multiply the first equation by $ -4 $ and add the result to the third equation. The result is:

$$\begin{array}{ cccc }~~ x&+~~9~ y&+~~7~ z&~=~1243\\&-~~~58~ y&-~~~48~ z&~=~-7986\\&-~~~29~ y&-~~~24~ z&~=~-3993\end{array}$$

Step 4: Divide the second equation by $ 2 $. The result is:

$$\begin{array}{ cccc }~~ x&+~~9~ y&+~~7~ z&~=~1243\\&-~~~29~ y&-~~~24~ z&~=~-3993\\&-~~~29~ y&-~~~24~ z&~=~-3993\end{array}$$

Step 5: Multiply the second equation by $ -1 $ and add the result to the third equation. The result is:

$$\begin{array}{ cccc }~~ x&+~~9~ y&+~~7~ z&~=~1243\\&-~~~29~ y&-~~~24~ z&~=~-3993\\&&0&~=~0\end{array}$$

Step 6: All the elements in the last row are zero, so the variable $ z $ can take any value, let

$$ \color{blue}{ z = t } $$

Step 7: Supstitute $ \color{blue}{ z = t } $ into second equation and solve for $ y $:

$$ \color{red}{y} = \frac{ 24 z - 3993 } { -29 } = \color{red}{ - \frac{ 24 }{ 29 } t + \frac{ 3993 }{ 29 } } $$

Step 8: Supstitute $ y = - \frac{ 24 }{ 29 } t + \frac{ 3993 }{ 29 } $ and $ z = t $ into first equation to find $ x $:

$$ \color{green}{x} = \frac{ 1243 - 9 \cdot y - 7 \cdot z } { 1 } = \color{green}{ \frac{ 13 }{ 29 } t + \frac{ 110 }{ 29 } }$$

System 3x3 calculator