Given the system of equation `a(x+y+z)=x, b(x+y+z)=y, c(x+y+z)= z` where `a,b,c` are non-zero real numbers.If the real numbers are such that `xyz!=0` ,then `(a+b+c)` is equal to

If the system of linear equations 2x + 2y +3z =a 3x - y +5z =b x- 3y +2z =c where a, b, c are non-zero real numbers, has more than one solution, then

If the system of linear equations 2x+2y+3z=a 3x-y+5z=b x-3y+2z=c where a,b and c are non-zero real numbers, has more than one solution, then

The system of equations -2x+y+z=a x-2y+z=b x+y-2z=c has

If x, y, z are positive real numbers such that x+y+z=a, then

The system of equations ax + y + z = 0 , -x + ay + z = 0 and - x - y + az = 0 has a non-zero solution if the real value of 'a' is

Consider the system of equations (a -1) x -y -z = 0 x -(b -1) y +z = 0 x + y - (c -1) z = 0 Where a, b and c are non-zero real number Statement1 : If x,y,z are not all zero, then ab + bc + ca + abc Statement 2 : abc ge 27

If a^(x)=b, b^(y)=c,c^(z)=a, prove that xyz = 1 where a,b,c are distinct numbers

If (xy)/(x+y)=a,(xz)/(x+z)=b and (yz)/(y+z)=c where a,b,c are other than zero,find the value of x

If a + x = b + y = c + z + 1 , where a, b,c,x,y,z are non polar distinct real numbers , then |(x, a+y,x + a),(y , b+y , y + b),(z,c+y, z+c)| is equal to :