# Prove that the lines 2x – 3y + 1 = 0, x + y = 3, 2x – 3y = 2 and x + y = 4 form a parallelogram.

Given: 2x – 3y + 1 = 0,

x + y = 3,

2x – 3y = 2

x + y = 4 are given equation

To prove:

The lines 2x – 3y + 1 = 0, x + y = 3, 2x – 3y = 2 and x + y = 4 form a parallelogram.

Explanation:

The given lines can be written as

… (1)

… (2)

… (3)

… (4)

The slope of lines (1) and (3) is 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.

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