what does x reduce to????

6x=15(mod 21)
2x=5(mod 7)

x= ?(mod)7

see solution below

To find the value of x (mod 7) in the given equations, you need to solve the congruences. Let's start with the first equation:

6x ≡ 15 (mod 21)

To find a solution for x, you can divide both sides of the congruence by their greatest common divisor (GCD). In this case, the GCD of 6 and 21 is 3, so we divide by 3:

2x ≡ 5 (mod 7)

Now, let's solve this second equation. The GCD of 2 and 7 is 1, so we can directly multiply both sides by the modular inverse of 2 (mod 7). The modular inverse of 2 (mod 7) is 4, as 2 * 4 ≡ 1 (mod 7). So we have:

x ≡ (5 * 4) ≡ 20 ≡ 6 (mod 7)

Therefore, x ≡ 6 (mod 7).