$3x\equiv7\pmod{11}, 5y\equiv9\pmod{11}$. 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.

$3x\equiv7\pmod{11}$ $\implies$ $12x\equiv28\pmod{11}$  $\implies$  $x\equiv6\pmod{11}$
$5y\equiv9\pmod{11}$ $\implies$  $45y\equiv81\pmod{11}$  $\implies$  $y\equiv4\pmod{11}$
Therefore
$x+y\equiv10\pmod{11}$
