GATE 2014 CS (CS1) – Question 14
Find the number of solutions of $3x+2y=1$, $4x+7z=1$, $x+y+z=3$, $x-2y+7z=0$.
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Correct answer: 1 to 1
Explanation
From3x+2y=1 and x+y+z=3 obtain y=(1−3x)/2 and z=(5+x)/2. Substitution in4x+7z=1 yields x=−11/5, then y=19/5,z=7/5. These also satisfy x−2y+7z=0. Therefore the system is consistent with **one solution**.