Prove that the lines `2x-3y+1=0,\ x+y=3,\ 2x-3y=2\ a n d\ x+y=4` form a parallelogram.

Prove that the three lines 2x-y-5=0, 3x-y-6=0 and 4x-y-7=0 meet in a point.

Prove that the lies 3x+y-14=0,\ x-2y=0\ n a d\ 3x-8y+4=0 are concurrent.

Prove that the three lines 5x+3y-7=0, 3x-4y=10, and x+2y=0 meet in a point.

Prove that the lines y=sqrt3x+1,\ y=4\ n d\ y=-sqrt3x+2 form an equilateral triangle.

If a ,\ b ,\ c are in A.P. prove that the straight lines a x+2y+1=0,\ b x+3y+1=0\ a n d\ c x+4y+1=0 are concurrent.

Write the angle between the lines 2x=3y=z\ a n d\ 6x=-y=-4zdot

Show that the area of the parallelogram formed by the lines 2x-3y+a=0,\ 3x-2y-a=0,\ 2x-3y+3a=0\ a n d\ 3x-2y-2a=0\ is(2a^2)/5s qdotu n i t sdot

If the points (-2,\ -1),\ (1,\ 0),\ (x ,\ 3) and (1,\ y) form a parallelogram, find the values of x and y .

Prove that the lines sqrt(3)x+y=0,\ sqrt(3)y+x=0,\ sqrt(3)x+y=1\ a n d\ sqrt(3)y+x=1 form a rhombus.

The lines 2x + y -1=0 , ax+ 3y-3=0 and 3x + 2y -2=0 are concurrent for -