Step 1: Convert all decimals to fractions

$$\begin{array}{ cccc }20~ x&-~~~8~ y&&~=~8\\-8~ x&+~~28~ y&-~~~15~ z&~=~0\\&-~~~15~ y&+~~25~ z&~=~-12\end{array}$$

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

$$\begin{array}{ cccc }5~ x&-~~~2~ y&&~=~2\\-8~ x&+~~28~ y&-~~~15~ z&~=~0\\&-~~~15~ y&+~~25~ z&~=~-12\end{array}$$

Step 3: Multiply the first equation by $ \frac{ 8 }{ 5 } $ and add the result to the second equation. The result is:

$$\begin{array}{ cccc }5~ x&-~~~2~ y&&~=~2\\&\dfrac{ 124 }{ 5 }~ y&-~~~15~ z&~=~\dfrac{ 16 }{ 5 }\\&-~~~15~ y&+~~25~ z&~=~-12\end{array}$$

Step 4: Get rid of the fractions by multiplying the second equation by 5. The result is:

$$\begin{array}{ cccc }5~ x&-~~~2~ y&&~=~2\\&124~ y&-~~~75~ z&~=~16\\&-~~~15~ y&+~~25~ z&~=~-12\end{array}$$

Step 5: Multiply the second equation by $ \frac{ 15 }{ 124 } $ and add the result to the third equation. The result is:

$$\begin{array}{ cccc }5~ x&-~~~2~ y&&~=~2\\&124~ y&-~~~75~ z&~=~16\\&&\dfrac{ 1975 }{ 124 }~ z&~=~-\dfrac{ 312 }{ 31 }\end{array}$$

Step 6: Get rid of the fractions by multiplying the third equation by 124. The result is:

$$\begin{array}{ cccc }5~ x&-~~~2~ y&&~=~2\\&124~ y&-~~~75~ z&~=~16\\&&1975~ z&~=~-1248\end{array}$$

Step 7: Solve for $ z $.

$$ \begin{aligned} 1975 ~ z & = -1248 \\ z & = -\dfrac{ 1248 }{ 1975 } \end{aligned} $$

Step 8: Solve for $ y $ using the second equation:

$$ \begin{aligned}124y-75z &= 16\\124y-75\cdot \left( -\frac{ 1248 }{ 1975 } \right) &= 16\\y &= -\dfrac{ 20 }{ 79 } \end{aligned}$$

Step 9: Solve for $ x $ by substituting $ y = -\dfrac{ 20 }{ 79 } $ and $ z = -\dfrac{ 1248 }{ 1975 } $ into the first equation.

System 3x3 calculator