XY=4n+3, YZ=2n-7, XZ=22

Choose one of the equations, then try and rewrite in terms of 1 Unknown, eg I've chosen XZ = 22 and am going to write it in terms of X

XZ = 22

Z = 22/X (this is writing Z in terms of X)

So ... X (22/X) = 22

22/X=22X

22 = 22X^2 ( * ^2 is to the power 2)

Therefore X = 1

And Z = 22

Use this to solve the remaining equations

1xY = 4n + 3

22Y = 2n - 7

Then rearrange and do simultaneous equations

22Y - 66 = 88n

22Y + 7 = 2n

-73 = 86n

n = - 73/86

It is very very likely that I have made a mistake somewhere here given the strange number I have for n but I spent far too long on this not to post it ahaha, even if the numbers are incorrect this is the general method I would follow