Step 1: Convert all decimals to fractions

$$\begin{array}{ cccc }-1~ x&-~~~5~ y&-~~~5~ z&~=~2\\4~ x&-~~~5~ y&+~~4~ z&~=~19\\~~ x&+~~5~ y&-~~~~~ z&~=~-20\end{array}$$

Step 2: Multiply the first equation by $ 4 $ and add the result to the second equation. The result is:

$$\begin{array}{ cccc }-1~ x&-~~~5~ y&-~~~5~ z&~=~2\\&-~~~25~ y&-~~~16~ z&~=~27\\~~ x&+~~5~ y&-~~~~~ z&~=~-20\end{array}$$

Step 3: Multiply the first equation by $ 1 $ and add the result to the third equation. The result is:

$$\begin{array}{ cccc }-1~ x&-~~~5~ y&-~~~5~ z&~=~2\\&-~~~25~ y&-~~~16~ z&~=~27\\&&-~~~6~ z&~=~-18\end{array}$$

Step 4: Divide the third equation by $ 6 $. The result is:

$$\begin{array}{ cccc }-1~ x&-~~~5~ y&-~~~5~ z&~=~2\\&-~~~25~ y&-~~~16~ z&~=~27\\&&-~~~~~ z&~=~-3\end{array}$$

Step 5: Solve for $ z $.

$$ \begin{aligned} -1 ~ z & = -3 \\ z & = 3 \end{aligned} $$

Step 6: Solve for $ y $ using the second equation:

$$ \begin{aligned}-25y-16z &= 27\\-25y-16\cdot 3 &= 27\\y &= -3 \end{aligned}$$

Step 7: Solve for $ x $ by substituting $ y = -3 $ and $ z = 3 $ into the first equation.

System 3x3 calculator