Question

The following system of linear equations

7x + 6y – 2z = 0

3x + 4y + 2z = 0

x – 2y – 6z = 0, has

(1) infinitely many solutions, (x, y, z) satisfying x = 2z

(2) no solution

(3) only the trivial solution

(4) infinitely many solutions, (x, y, z) satisfying y = 2z

Answer 1

Answer is (1)

7x + 6y - 2z = 0 .... (1)

3x + 4y + 2z = 0 .... (2)

x - 2y - 6z = 0 .... (3)

⇒ infinite solutions

Now (1) + (2) ⇒ y = –x put in (1), (2) & (3) all will lead to x = 2z

Answer 2

Answer is (1)