Congruent question with multiple congruence conditions?

Question

Say if x ≡ 3 (mod 7) and y ≡ 5 (mod 7)

How would I use the above given information to solve the problems below?

• xy ≡ 4 (mod 7)
• x ≡ y (mod 7)

If you could explain it, that would be greatly appreciated, thanks :)

Answer 1

$$a\equiv b\pmod m,c\equiv d\pmod m$$

$$\implies ac-bd=a(c-d)+d(a-b)\equiv0\pmod m\implies ac\equiv bd\pmod m$$

Set $a=x,c=y,b=3,d=5$

Find $\#8$ of this