 Hello friends welcome to the session and we are going to discuss how to form the pair of linear equations in the following problems and find the solutions if they exist by any algebraic method. Our problem is the area of 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. So, let us start with the solution. We all know that the area of rectangle equal to length into breadth either behind the question rectangle v x units of the rectangle v y units area equal to x y unit square. Now according to question reduced by 5 units that is x minus 5 and breadth is increased by 3 units that is y plus 3 then area which is x y is reduced by 9 square units. So, this implies x y plus 3 x minus 5 y minus 15 equal to x y minus 9 this implies x y x y cancel out 3 x minus 5 y minus 15 plus 9 equal to 0 this implies 3 x minus 5 y minus 6 equal to 0 this is our first equation. Now again from the question according to question is increased by 3 units and breadth is increased by 2 units then area is increased by 67 square units this implies x y plus 2 x plus 3 y plus 6 equal to x y plus 67 this implies x y x y cancel out 2 x plus 3 y minus 61 equal to 0 this is our second equation thus the two equations are minus 5 y minus 6 equal to 0 this is our first equation and 2 x plus 3 y minus 61 equal to 0 this is our second equation. Now multiply equation first by 2 second by 3 we get into 3 x minus 2 into 5 y minus 2 into 6 which is 12 equal to 0 this is our third equation which can be written as 6 x minus 10 by minus 12 equal to 0 similarly we multiply equation second by 3 this will give us 6 x plus 9 by minus 183 equal to 0 this is our fourth equation. Now subtracting equation minus 6 x 9 by minus of minus 10 by minus 183 minus of minus 12 equal to 0 this implies 0 plus 9 by plus 10 by minus 183 plus 12 equal to 0 this implies 19 by equal to 171 this implies y equal to 171 upon 19 this implies y equal to 9 units. Now we will substitute the value of y in equation third. Our equation third is 6 x minus 10 by minus 12 equal to 0 now we will substitute y equal to 9 this will give us 6 x minus 10 into 9 minus 12 equal to 0 this implies 6 x minus 90 minus 12 equal to 0 this implies 6 x equal to 102 this implies x equal to 102 upon 6 this implies x equal to 17 units hence the equations are 3 x minus 5 by minus 6 equal to 0 and 2 x plus 3 by minus 61 equal to 0 where x and y are respectively the length and breadth in units of the rectangle length which is x equal to 17 breadth y equal to 9 hope you understood the solution and enjoyed the session goodbye and take care.