I'm looking at this example and it doesn't make sense to me.
We have to solve the following systems of linear congruences :
$x\equiv 1\pmod 5$
$x\equiv 2\pmod 6$
$x\equiv 3\pmod 7$
We take congruence no. 1 as $x=5t+1$.
We plug it into the second one :
$5t + 1\equiv 2\pmod 6$
- Now, how do we get from that to $t\equiv 5\pmod 6$ ?
Next, we make the $t = 6u + 5$
The equation now becomes $30u + 26$
We plug this into the third congruence :
$30u + 26\equiv 3\pmod 7$
- Now, how do we get from that to $u\equiv 6\pmod 7$ ?