Step 1. First substitute in equations (2) and (4) with the expression given in the equation (3).
Step 2. Next, in the equation (5) express . Use that expression as a substitution for in equation (4). Now equation (4) should represent in terms of z's, k's and Y(z).
Step 3. Next use the expression for in equation (4) as a substitution for in equation (1). Now equation (1) should give you the expression for in terms of z's,k's and X(z) and Y(z).
Now you have to deal with the equation (2). Substitute with the expression in the equation (1) from the step 3. On the left side of the equation term substitute with the expression obtained from the equation (5) (see step 2.)
After that that equation should contain no V's and I presume thats the equation you've been chasing all along?