GATE 2026 ST – Question 39
Consider x+2y−z=a,x+y+3z=b,2x+3y+2z=c. I:a solution exists for every (a,b,c)∈ℝ³. II:for (a,b,c)=0 the solutions are {(−7t,4t,t):t∈ℝ}. Which hold?
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Correct answer: (B) Only II correct
Explanation
The third left side is the sum of the first two, so consistency requires c=a+b, refuting I. For zero right sides, subtraction gives y=4z and then x=−7z. Write z=t to obtain precisely the listed line. **B**.