Question:

If $3x + 4y = 12$ and $x - y = 1$, what is the value of $x + y$?

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Simultaneous equations can be solved by substitution or elimination. Always verify by substituting back.

CAT - 2012
CAT

Updated On: Aug 1, 2025

24/7
25/4
25/7
23/7

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The Correct Option is C

Solution and Explanation

Step 1: From the Second Equation

From x − y = 1:

x = y + 1

Step 2: Substitute into the First Equation

Substituting x = y + 1 into 3x + 4y = 12:

3(y + 1) + 4y = 12 3y + 3 + 4y = 12 7y + 3 = 12 7y = 9 y = 9/7

Step 3: Find x

Using x = y + 1:

x = (9/7) + 1 = (9/7) + (7/7) = 16/7

Step 4: Find x + y

Adding the values:

x + y = (16/7) + (9/7) = 25/7

Final Answer:

x + y = 25/7

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