Question

The system of equations
$x+y+z=0$
$2x+3y+z=0$
$x+2y=0$
has

• A. a unique solution; $x=0,y=0,z=0$
• B. infinite solutions
• C. no solution
• D. finite number of non-zero solutions

Answer 1

Answer: (B)

x + y + z = 0...(1)
2x + 3y + z = 0 ...(2)
x + 2y = 0 ... (3)
From equation (3), we have
x = - 2y
Putting this value of x in equations (1), we
get - 2y + y + z = 0 $\Rightarrow$ y = z
Hence x = - 2z
Thus, the solution of the given system of equations is (-2z, z, z), where z is a parameter (Z $\in$ R). Hence the system has infinite number of solutions including zero solution.