 Hello friends, welcome to the session and Malkavi 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. The problem is places A and B are 100 km apart on a highway, one car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours, if they travel towards each other they meet in 1 hour. What are the speeds of the two cars? Now let's start with the solution. Now here we are given that we have to find the speed and we all know that speed equal to distance upon time. This is the basic idea behind the question. Now let us assume that y v two cars starting from points respectively speed v km per hour. Now one integration two cars move in the same direction. So now suppose two cars meet at the point q then a car x equal to a q is traveled by car y equal to v q. Now it is given in the question that two cars meet in 5 hours therefore distance into time which is equal to 5 u km. Similarly 7 y equal to speed into time which is equal to 5 v km. Now equal to a q minus v q since a v is 100 a q is 5 u minus 5 v we can say 5 v equal to 100 minus v equal to 20. This is our first equation. Now we consider the second case that is when two cars move in opposite direction. Now suppose the two cars meet at the point p therefore distance to a p which is given by into time is equal to u into 1. Since we are given that the two cars meet in 1 hour. Now v p equal to speed into time km also 1 since we are given that two cars meet in 1 hour. Now u plus v p equal to a p this implies u plus v equal to 100 u plus v equal to 100 is our second equation. Thus the two equations are minus v equal to 20 this is our first equation and u plus v equal to 100 is our second equation. Now adding equation equal to 120 this implies u equal to 120 upon 2 which is equal to 60. Now substituting u equal to 60 in equation first we get our equation first is u minus v equal to 20. Where we will substitute u equal to 60 this implies 60 minus v equal to 20 this implies minus v equal to 20 minus 60 this implies minus v equal to minus 40 this implies v equal to 40. Therefore the equations are u minus v equal to 20 and u plus v equal to 100 where u and v are the speeds in km per hour of the two cars u equal to 60 and v equal to 40 which is a required solution hope you understood it and enjoy the session goodbye and take care.