 Hello friends, welcome to the session. I am Malika. We are going to discuss pair of linear equations in two variables. A given question is form the pair of linear equations in the following problems and find the solutions if they exist by any algebraic method. A given problem is a part of monthly hostel charges specs and the remaining depends on the number of days one has taken food in the mess. When a student A takes food for 20 days she has to pay rupees 1000 as hostel charges whereas a student B who takes food for 26 days pays rupees 1180 as hostel charges. Find the fixed charges and the cost of food per day. So let's start with the solution. From the question we see that there are two unknowns. First is the fixed charges and second is the cost of the food. So let us assume let the fixed charge be rupees X and let the per day charge be rupees Y. Now from the question we see that for student A she pays rupees 1000 for 20 days therefore charges for 20 days equal to rupees 20 Y. Now according to question which is the fixed charge plus charges of 20 days which is 20 Y equal to 1000 rupees for a student. So let this be our first equation. Now for student B according to question we see that student B pays rupees 1180 for 26 days. Therefore charges for 26 days be rupees 26 Y. Now according to question which is the fixed charge plus charges for 26 days which is 26 Y equal to 1180. So let this be our second equation. Thus the two equations are X plus 20 Y equal to 1000 and X plus 26 Y equal to 1180. Now this is our first equation and this is our second equation. So from equation first we get X equal to 1000 minus 20 Y. Now we will substitute the value of X in equation second. Our equation second is X plus 26 Y equal to 1180. Now we will substitute the value of X which is 1000 minus 20 Y plus 26 Y equal to 1180. This implies 1000 minus 20 Y plus 26 Y equal to 1180. This implies 6 Y equal to 1180 minus 1000. This implies Y equal to 180 upon 6. This implies Y equal to 30. Now we will substitute the value of Y in equation third which is X equal to 1000 minus 20 Y. Here we will substitute Y equal to 30. This implies X equal to 1000 minus 20 into 30. This implies X equal to 1000 minus 600. This implies X equal to 400. Hence the equations are X plus 20 Y equal to 1000 and X plus 26 Y equal to 1180 where X is fixed charge Y is charge for food per day. This is fixed charge equal to 400 and Y which is a charge for food per day is 30 rupees. Hope you understood the solution and enjoyed the session. Goodbye and take care.