$3x\equiv7\pmod{11}, 5y\equiv9\pmod{11}$. Find the number which $x+y\pmod{11}$ is congruent to. Given that $3x\equiv7\pmod{11}, 5y\equiv9\pmod{11}$. Find the number which $x+y\pmod{11}$ is congruent to. I'm thinking $20\equiv9\pmod{11}$, But I am having trouble find a number $3x$ that  is divisible by $3$? Is there a better way of solving this problem.

3x $\equiv$ 7 (mod 11) and 5y $\equiv$ 9 (mod 11)
3x $\equiv$ 18 (mod 11) by adding 11 to 7, then 5y $\equiv$ 20 (mod 11) by add 11 to 9.
x $\equiv$ 6 (mod 11) by dividing 3 to both sides, then y $\equiv$ 4 (mod 11) by dividing 5 to both sides.
Then, x + y $\equiv$ 10 (mod 11)
