If a system of three linear equations `x+4a y+a=0,x+3b y+b=0,a n dx+2c y+c=0` is consistent, then prove that `a ,b , c` are in H.P.

If the equation 2x+3y+1=0,3x+y-2=0, and ax+2y-b=0 are consistent,then prove that a-b=2

If equations a^2x+b^2y+c^2=0,a^4x+b^4y+c^4=0 and x+y+1=0 are consistent then

If c<1 and the system of equations x+y-1=0,2x-y-c=0, and bx+3by-c=0 is consistent,then the possible real values of b are b epsilon(-3(3)/(4))quad b.b epsilon(-(3)/(2),4) c.be (-(3)/(4),3) d.none of these

If the lines x+a y+a=0,\ b x+y+b=0\ a n d\ c x+c y+1=0 are concurrent, then write the value of 2a b c-a b-b c-c adot

If c lt 1 and the system of equations x+y-1=0 2x-y-c=0 and -bx+3by-c =0 is consistent then the possible real values of b are

If x =a, y=b, z=c is a solution of the system of linear equations x + 8y + 7z =0, 9 x + 2y + 3z =0, x + y+z=0 such that point (a,b,c ) lies on the plane x + 2y + z=6, then 2a+ b+c equals

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

If x=a,y=b,z=c is a solution of the system of linear equations x+8y+7z=0,9x+2y+3z=0,x+y+z=0 such that the point (a,b,c) lies on the plane x+2y+z=6, then 2a+b+c equal to