Solve the system of equations : `z+ay+a^2x+a^3=0 z+by+b^2x+b^3=0 z+cy+c^2x+c^3=0]` where `a != b != c.`

Solve the system of equations 2x+3y-3z=0 , 3x-3y+z=0 and 3x-2y-3z=0

Solve the system of equations 2x+3y-3z=0 , 3x-3y+z=0 and 3x-2y-3z=0

Solve the system of equations 2x+3y-3z=0 , 3x-3y+z=0 and 3x-2y-3z=0

Solve the system of equations 2x+3y-3z=0 , 3x-3y+z=0 and 3x-2y-3z=0

Solve the system of the equations: a x+b y+c z=d , a^2x+b^2y+c^2z=d^2 , a^3x+b^3y+c^3z=d^3 .

Solve the system of the equations: a x+b y+c z=d , a^2x+b^2y+c^2z=d^2 , a^3x+b^3y+c^3z=d^3 .

Solve the system of the equations: a x+b y+c z=d a^2x+b^2y+c^2z=d^2 a^3x+b^3y+c^3z=d^3 Will the solution always exist and be unique?

The solution of the system of equations a^(2)x+ay+z=-a^(3),b^(2)x+by+z=-b^3, c^2x+cy +z=-c^(3) is (A) x=-(a+b+c),y=ab+bc+ca,z=-abc (B) x=(a+b+c),y=ab+bc+ca,z=-abc (C) x=-(a-b-c),y=ab+bc+ca,z=-abc (D) None of these

If the system of equations ax + by + c = 0,bx + cy +a = 0, cx + ay + b = 0 has infinitely many solutions then the system of equations (b + c) x +(c + a)y + (a + b) z = 0(c + a) x + (a+b) y + (b + c) z = 0(a + b) x + (b + c) y +(c + a) z = 0 has