Since y is already missing in the middle equation, we will
eliminate y from the other two equations:



To make the y's cancel we multiply the first one through by 5



Adding corresponding terms causes the y's to cancel:



Now we put that with the original middle equation that
already had y eliminated:



To make the x's cancel we multiply the second one through by -3:



Adding corresponding terms causes the x's to cancel:




Substitute that in 






Substitute that and  in one of the original
three equations, that contains a y:







So the solution is (x,y,z) = (0,1,4)

Edwin