Isolate one of the variables from one of the equations. Let's say you have the system (1) x - 5y - 11z = 698, (2) x - 4y - 3z = 299, and (3) -x + 9y - 7z = -94. If you solve (1) for x, in terms of y and z, you can plug the solved value of x into (2) and (3) to obtain two-variable systems. Solved for x, (1) becomes (4) x=698+5y+11z.
Plug (4) into (2). You will obtain 698+5y+11z-4y-3z=299. Simplified, this becomes (5) y+8z=-399.
Plug (4) into (3) to get -698-5y-11z+9y-7z=-94. Simplification gives (6) 4y-18z=604.
Solve (5) for y to get y=-8z-399. Plug it into (6), to get -32z-1596-18z=604. Simplification gives the result -50z=2200, or z=-44.
Plug the value of z into (5) or (6) to find the numerical value of y. Plugging into (5) gives y=-8*-44-399 (in which -8 is multiplied by -44, and -399 is subtracted). Finding y in this way delivers y=-47, for the solution.
Plug your values of y and z into either of the first equations to solve for x. Since x=698+5y+11z, or 698+5*-47+11*-44, x=-21.