Question:
What is the value of 'x'?
I) $x+2y=6$
II) $3x+6y=18$
What is the value of 'x'?
I) $x+2y=6$
II) $3x+6y=18$
I) $x+2y=6$
II) $3x+6y=18$
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If one equation is a direct multiple of another, they do not provide new information.
Updated On: Jun 26, 2026
- Statement I alone is sufficient
- Statement II alone is sufficient
- Statements I and II together are sufficient
- Statements I and II together are not sufficient
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The Correct Option is D
Solution and Explanation
Step 1: Concept
Two linear equations are sufficient for two variables only if they are independent.
Step 2: Analysis of Statement I
$x + 2y = 6$. One equation, two variables. Infinitely many solutions for $x$. Not sufficient.
Step 3: Analysis of Statement II
$3x + 6y = 18$. Divide by 3: $x + 2y = 6$. Same as Statement I. Not sufficient.
Step 4: Combined Analysis
Since Statement II is just a multiple of Statement I, they are "dependent" and represent the same line. There is still no unique value for $x$.
Step 5: Conclusion
Correct choice is (4). Final Answer: (4)
Two linear equations are sufficient for two variables only if they are independent.
Step 2: Analysis of Statement I
$x + 2y = 6$. One equation, two variables. Infinitely many solutions for $x$. Not sufficient.
Step 3: Analysis of Statement II
$3x + 6y = 18$. Divide by 3: $x + 2y = 6$. Same as Statement I. Not sufficient.
Step 4: Combined Analysis
Since Statement II is just a multiple of Statement I, they are "dependent" and represent the same line. There is still no unique value for $x$.
Step 5: Conclusion
Correct choice is (4). Final Answer: (4)
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