If x ≡ 4 (mod 7) and y ≡ 3 (mod 7), what is the value of (x + y) mod 7?

₹0.0

Question: If x ≡ 4 (mod 7) and y ≡ 3 (mod 7), what is the value of (x + y) mod 7?

Options:

Correct Answer: 0

Solution:

x + y ≡ 4 + 3 ≡ 7 (mod 7), which is equivalent to 0.

If x ≡ 4 (mod 7) and y ≡ 3 (mod 7), what is the value of (x + y) mod 7?

If x ≡ 4 (mod 7) and y ≡ 3 (mod 7), what is the value of (x + y) mod 7?

Step 1: Understand what 'x ≡ 4 (mod 7)' means. This means when you divide x by 7, the remainder is 4.
Step 2: Understand what 'y ≡ 3 (mod 7)' means. This means when you divide y by 7, the remainder is 3.
Step 3: Add the two values: 4 (from x) + 3 (from y) = 7.
Step 4: Now, we need to find (x + y) mod 7. We take the result from Step 3, which is 7.
Step 5: Calculate 7 mod 7. When you divide 7 by 7, the remainder is 0.
Step 6: Therefore, (x + y) mod 7 = 0.

Modular Arithmetic – Understanding how to perform addition and find the result under a modulus.
Congruences – Using congruences to simplify calculations in modular arithmetic.