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JEE MAIN Mathematics QUESTION #976
Question 1
If the system of linear equations \(x+y+2z=6\), \(2x+3y+az=a+1\), \(-x-3y+bz=2b\), where \(a,b\in\mathbb{R}\), has infinitely many solutions, then \(7a+3b\) is equal to:
  • 16✔️
  • 12
  • 22
  • 9
Correct Answer Explanation
For infinitely many solutions, the determinant of coefficient matrix \(=0\) and the augmented matrix is consistent. Solving the determinant condition and consistency condition gives \(a\) and \(b\), then \(7a+3b=16\).