There are any number of ways to proceed with the computations. One way might to be subtract the third equation from the first, eliminating "y". Then multiply the third equation by 3, and add to the second equation, again eliminating "y". This will give you two equations in just two variables, being "x" and "z".
Assuming the "27" in the second equation is a typo for "2z", you should be able to solve one of the new equations for "x=". Substitute the result into the other new equation, and solve for the value of "z". Back-solve for "x", and then again for "y".
If you get stuck, please reply showing your work and reasoning so far. Thank you!