Firstly, the ternary linear equation is transformed into the binary linear equation, and the best starting point of the three groups of equations is the second group: y-3z=-4, then y = 3z-4;

Substituting it into the other two equations, we get:

X-(3z-4)-2z= 10，x-5z=6。

3x-(3z-4)+5z=2 1 equals 3x+2z= 17.

Multiply the first equation by 3 and subtract the second equation to get 3x-15z-3x-2z =18-17, and z =-117.

So x = 97/ 17, y =-7117.

The above is the solution of this equation. The verification method is to substitute these three values into any equation in the problem and confirm whether the left and right are equal.