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sequences - recurrence relation

I have to find the expression of $(y_n)$ defined by :

$$y_{n+1}=a y_n+b z_n+c$$

where $(z_n)$ is an arithmetico-geometric sequence :

$$z_{n+1}=d z_n+e$$

and $a,b,c,d,e$ real numbers.

Thank you for your help.