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

Explanation

`2x – 3y + 1 = 0, x + y = 3, 2x – 3y = 2 x + y = 4` are given equation

Let it be (i) and (ii)


The slope of lines (1) and (3) is 2/3 and that of lines (2) and (4) is − 1.

Thus, lines (1) and (3), and (2) and (4) are two pair of parallel lines.
If both pair of opposite sides are parallel then,


we can say that it is a parallelogram.
Hence proved, the given lines form a parallelogram.