Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method

The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle.

#### Solution

Let length and breadth of rectangle be x unit and y unit respectively.

Area = xy

According to the question,

(x - 5) (y + 3) = xy - 9

⇒ 3x - 5y - 6 = 0 ... (i)

(x + 3) (y + 2) = xy + 67

⇒ 2x - 3y - 61 = 0 ... (ii)

By cross multiplication, we get

`x/(305-(-18)) = y/(-12-(-183)) = 1/(9-(-10))`

`x/323 = y/171 = 1/19`

x = 17, y = 9

Hence, the length of the rectangle = 17 units and breadth of the rectangle = 9 units.