Solve system of equations using Elimination method

$$\begin{array}{ cccc }60~ x&+~~40~ y&+~~50~ z&~=~3900\\150~ x&+~~100~ y&+~~200~ z&~=~11250\\24~ x&+~~16~ y&+~~23~ z&~=~1620\end{array}$$

Step 1: Convert all decimals to fractions

$$\begin{array}{ cccc }60~ x&+~~40~ y&+~~50~ z&~=~3900\\150~ x&+~~100~ y&+~~200~ z&~=~11250\\24~ x&+~~16~ y&+~~23~ z&~=~1620\end{array}$$

Step 2: Divide the first equation by $ 10 $. The result is:

$$\begin{array}{ cccc }6~ x&+~~4~ y&+~~5~ z&~=~390\\150~ x&+~~100~ y&+~~200~ z&~=~11250\\24~ x&+~~16~ y&+~~23~ z&~=~1620\end{array}$$

Step 3: Divide the second equation by $ 50 $. The result is:

$$\begin{array}{ cccc }6~ x&+~~4~ y&+~~5~ z&~=~390\\3~ x&+~~2~ y&+~~4~ z&~=~225\\24~ x&+~~16~ y&+~~23~ z&~=~1620\end{array}$$

Step 4: Swap Row 1 and Row 2. The result is:

$$\begin{array}{ cccc }3~ x&+~~2~ y&+~~4~ z&~=~225\\6~ x&+~~4~ y&+~~5~ z&~=~390\\24~ x&+~~16~ y&+~~23~ z&~=~1620\end{array}$$

Step 5: Multiply the first equation by $ -2 $ and add the result to the second equation. The result is:

$$\begin{array}{ cccc }3~ x&+~~2~ y&+~~4~ z&~=~225\\&&-~~~3~ z&~=~-60\\24~ x&+~~16~ y&+~~23~ z&~=~1620\end{array}$$

Step 6: Multiply the first equation by $ -8 $ and add the result to the third equation. The result is:

$$\begin{array}{ cccc }3~ x&+~~2~ y&+~~4~ z&~=~225\\&&-~~~3~ z&~=~-60\\&&-~~~9~ z&~=~-180\end{array}$$

Step 7: Divide the second equation by $ 3 $. The result is:

$$\begin{array}{ cccc }3~ x&+~~2~ y&+~~4~ z&~=~225\\&&-~~~~~ z&~=~-20\\&&-~~~9~ z&~=~-180\end{array}$$

Step 8: Divide the third equation by $ 9 $. The result is:

$$\begin{array}{ cccc }3~ x&+~~2~ y&+~~4~ z&~=~225\\&&-~~~~~ z&~=~-20\\&&-~~~~~ z&~=~-20\end{array}$$

System 3x3 calculator