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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?
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If x ≡ 4 (mod 7) and y ≡ 3 (mod 7), what is the value of (x + y) mod 7?
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x + y ≡ 4 + 3 ≡ 7 (mod 7), which is equivalent to 0.
Questions & Step-by-step Solutions
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Q
Q: If x ≡ 4 (mod 7) and y ≡ 3 (mod 7), what is the value of (x + y) mod 7?
Solution:
x + y ≡ 4 + 3 ≡ 7 (mod 7), which is equivalent to 0.
Steps: 6
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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.
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