First use Gaussian elimination to rewrite the system in row-echelon form.
Solve for y in terms of z, to obtain
By back substituting y=4-7z into Equation 1, we can solve for x:
Finally, let z=a, where a is a real number, and you have the solution
x=8-5a y=4-7a z=a
So, every ordered triple in the form of
(8-5a, 4-7a, a) where a is a real number, is a solution of the system.
There are infinite solutions to this system.