Let the length and breadth of the rectangle be x and y units respectively. Then,Area \\\\(=xy\\\\) sq. units.If length is reduced by \\\\(5\\\\) units and the breadth is increases by \\\\(3\\\\) units, then area is reduced by \\\\(9\\\\) square units.\\\\(\ herefore xy-9=(x-5)(y+3)\\\\)\\\\(\\Rightarrow xy-9=xy+3x-5y-15\\\\)\\\\(\\Rightarrow 3x-5y-6=0\\\\) ...(i)When length is increased by \\\\(3\\\\) units and breadth by \\\\(2\\\\) units, the area is increased by \\\\(67\\\\) sq. units.\\\\(\ herefore xy+67=(x+3)(y+2)\\\\)\\\\(\\Rightarrow xy+67=xy+2x+3y+6\\\\)\\\\(\\Rightarrow 2x+3y-61=0\\\\) ...(ii)Thus, we get the following system of linear equations:\\\\(3x-5y-6=0\\\\)\\\\(2x+3y-61=0\\\\)By using cross-multiplication, we have\\\\(\\dfrac{x}{305+18}=\\dfrac{-y}{-183+12}=\\dfrac{1}{9+10}\\\\)\\\\(\\Rightarrow x=\\dfrac{323}{19}=17\\\\) and \\\\(y=\\dfrac{171}{19}=9\\\\)Hence, the length and breadth of the rectangle are \\\\(17\\\\) units and \\\\(9\\\\) units respectively.