You can solve this by using the two equations with the z to create a fourth equation. Get the z's to equal each other my multiplying the whole equation by factors that would do so. Then subtract them from each other to get it to cancel out. Then you can use that equation along with the middle equation to solve for either x or y in the same way. Once you have one answer, you can use the middle equation to find the second one and any equation to find z.
