I have a system of differential equations which I need to solve and obtain y(x) and z(x). I tried elimination method and got to a point but I don't know what to do after here. Any help would be appreciated Question:

$${y}^{\prime}(x)=\frac{x+y}{z}$$

$${z}^{\prime}(x)=\frac{x-y}{y}$$

$${y}^{\prime}(x)=\frac{x+y}{z}$$

$${z}^{\prime}(x)=\frac{x-y}{y}$$