If the equation `2x+3y+1=0,3x+y-2=0,a n da x+2y-b=0` are consistent, then prove that `a-b=2.`

x-3y=1,3x-2y+4=0

If the system of equations x+a y=0,a z+y=0,a n da x+z=0 has infinite solutions, then the value of equation has no solution is -3 b. 1 c. 0 d. 3

Show that the equations -2x+y+z=a,x-2y+z=b,x+y-2z=c are consistent only if a+b+c=0.

If the lines 3x + 4y+ 1 = 0, 5x +lambda y + 3 = 0 and 2x + y-1 = 0 are concurrent, then lambda=

If the straight lines 2x+3y-1=0,x+2y-1=0 ,and a x+b y-1=0 form a triangle with the origin as orthocentre, then (a , b) is given by (a) (6,4) (b) (-3,3) (c) (-8,8) (d) (0,7)

The straight lines x+2y-9=0,3x+5y-5=0 , and a x+b y-1=0 are concurrent, if the straight line 35 x-22 y+1=0 passes through the point (a) (a , b) (b) (b ,a) (c) (-a ,-b) (d) none of these

Find k if the equations x+2y+2z=0, x-3y-3z=0, 2x+y+kz=0 have only the trivial solution.

The line 2x+3y=5 , 2x+y=k , 2x-y-1=0

If the join of (x_1,y_1) and (x_2,y_2) makes on obtuse angle at (x_3,y_3), then prove than (x_3-x_1)(x_3-x_2)+(y_3-y_1)(y_3-y_2)<0

Find lambda for which the system of equations x+y-2z=0,2x-3y+z=0,x-5y+4z=lambda is consistent and find the solutions for all such values of lambdadot