Verified Solution • 2025–26 Session
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QJEEM20Ma631e: JEE Main 2020 Mathematics - Class 12 JEEM20Ma631e Solution: The following system of linear equations 7x + 6y – 2z = 0 3x +…
The following system of linear equations
7x + 6y – 2z = 0
3x + 4y + 2z = 0
x – 2y – 6z = 0, has
7x + 6y – 2z = 0
3x + 4y + 2z = 0
x – 2y – 6z = 0, has
Multiple Choice Options
- A no solution
- B infinitely many solutions, (x, y, z) satisfying y = 2z
- C infinitely many solutions, (x, y, z) satisfying x = 2z
- D only the trivial solution
Step-by-Step Verified Solution
Given
7x + 6y – 2z = 0 .......(1)
3x + 4y + 2z = 0 ......(2)
x – 2y – 6z = 0 .......(3)
=
= 7(–24 + 4) – 6(–18 – 2) – 2(–6 – 4) = 0
= 0
The system of equation has infinite non-trival solution.
Also adding equation (1) and 3 (3), we get
10x = 20z
x = 2z
7x + 6y – 2z = 0 .......(1)
3x + 4y + 2z = 0 ......(2)
x – 2y – 6z = 0 .......(3)
=
= 7(–24 + 4) – 6(–18 – 2) – 2(–6 – 4) = 0
= 0
The system of equation has infinite non-trival solution.
Also adding equation (1) and 3 (3), we get
10x = 20z
x = 2z