 Hello friends, welcome to the session. I am Alka. We are going to discuss pair of linear equations in two variables. A given question is, Aftab tells his daughter, 7 years ago, I was 7 times as old as you were then. Also, 3 years from now, I shall be 3 times as old as you will be. Isn't this interesting? We have to represent this situation algebraically and graphically. Now, before starting with the solution, I would like to tell you the basic idea behind the question. That is, a pair of linear equations in two variables, the x and y, can be represented algebraically as A1x plus B1y plus C1 equal to 0 and A2x plus B2y plus C2 equal to 0. Graphically, these two equations represent a pair of straight lines. Now, let's start with the solution. From the question we see that there are two unknowns, Aftab h and his daughter's h. So, first of all, let us assume their ages. Let the present age equal to x years. Let the present age of daughter equal to y years. Now, we see that 7 years ago, Aftab was, was, present age minus 7 years. Similarly, 7 years ago, daughter was present age minus 7 years. Now, according to the question, that was 7 times as old as his daughter, so this can be written as Aftab h was 7 times his daughter's age. Or this can be written as x minus 7 equal to 7y minus 49. This is equal to x minus 7y minus 7 plus 49 equal to 0 or x minus 7y plus 42 equal to 0. So, this is our first equation. Now, again from the question we see that it is given that 3 years from now, 3 years from now Aftab will be present age plus 3 years and daughter will be present age plus 3 years. Now, according to the question, it is given that 3 times his daughter's age. Or this can be written as x plus 3 equal to 3y plus 9 or x minus 3y plus 3 minus 9 equal to 0 or x minus 3y minus 6 equal to 0. Let this be our second equation. Hence, the algebraic representation of the situation is x minus 7y plus 42 equal to 0 and x minus 3y minus 6 equal to 0. Now, we will see the graphical representation of the given situation. We see that the two equations are x minus 7y plus 42 equal to 0 and x minus 3y minus 6 equal to 0. Now, we will find the two solutions for each equation. Now, for our first equation, when we take x equal to 0, we get y equal to 6 and on taking x equal to minus 7, we get y equal to 5. Now, we will solve the second equation for x and y. Now, if we take x equal to minus 3, we get y equal to minus 3 and on taking x equal to 6, we get y equal to 0. Now, thus we see that the points A with coordinates 0 and 6 B with coordinates minus 7 and 5 represent the equation x minus 7y plus 42 equal to 0 and the points C with coordinates minus 3 and minus 3 and D with coordinates 6 and 0 represent the equation minus 3y minus 6 equal to 0. Now, we plot these points A, B, C and D on the graph. Here is the graph with x-axis and y-axis and the scale we have taken for x-axis and y-axis is 1 centimeter equal to 2 units. Now, we plot the points A, B, C and D, A with coordinates 0 and 6. So, let this be the A point with coordinates 0 and 6, B with coordinates minus 7 and 5. So, it will be B minus 7 and 5 C with coordinates minus 3 and minus 3 D with coordinates 6 and 0. Now, we will join the points A, B, C and D carefully. Thus, we see that the pink line represents the equation x minus 7y equal to minus 42 and the yellow line represents the equation x minus 3y equal to 6. Now, on further producing these lines, they will meet at the point B. So, we can say that thus the two lines A, B and C intersect at the point B with coordinates 42 and 12. Hope you understood the solution and enjoyed the session. Goodbye and take care.