How do I prove that the following is a presentation of $\mathbb{Z_{35}}$? Prove that $\mathbb{Z_{35}}$ is isomorphic to $G=\langle x, y \, | \, x^7 = y^5 = 1, xyx^{-1}y^{-1}=1\rangle$. I'm having a very difficult time with such problems and would be very thankful to anyone who would take the time to slowly explain how does one even begin to take a stab at answering such a question. Thank you for your help.

$35 =7\cdot5$ , the Chinese remainder theorem show that $\mathbb{Z}_{35}\simeq\mathbb{Z}_7\times \mathbb{Z}_5$. Take u = a generator of $\mathbb{Z}_7$ and v a generator of $\mathbb{Z}_5$ and set x=(u,0) and y =(0,v)
