 Hi friends welcome to the session. I am Alka and today we are going to solve a problem based on pair of linear equation in two variables. Our question is solve the following pair of linear equation by the elimination method and the substitution method. Our given equations are 3x minus 5y minus 4 is equal to 0 and 9x is equal to 2y plus 7. So let's start with the solution. Our method will start with elimination method first. We are given with these two equations 3x minus 5y minus 4 is equal to 0 and 9x is equal to 2y plus 7. Now we will further solve them. We can write 3x minus 5y is equal to 4 and name it as our first equation then 9x minus 2y is equal to 7 and this is our second equation. Now we will multiply both the sides of equation number 1 by 3. On multiplying equation number 1 by 3 we get 9x minus 15y is equal to 12. We name this equation as our third equation. Now further we see that our equation number for a second and third on subtracting on subtracting equation second from third we get 9x minus 15y is equal to 12 and we will subtract 9x minus 2y is equal to 7. This will get cancelled out and from 15y we have to subtract 2. This will give minus 13y is equal to or subtracting 7 from 12 we get 5. This gives the value of y. This implies y is equal to minus 5 upon 13. Now on substituting the value of y is equal to minus 5 upon 13 in equation first. Our equation first is 3x minus 5y is equal to 4. We will place the value of y here and get 3x minus 5 minus 5 upon 13 is equal to 4. This implies 3x plus 25 upon 13 is equal to 4 which gives 3x is equal to 4 minus 25 upon 13. We will take the LCM 13 3x is equal to 13 is the LCM here 52 minus 25 which further implies 3x is equal to 27 upon 13. This implies x is equal to 27 upon 13 into 1 upon 3 which can be written as x is equal to 27 upon 39 or we can cancel 27 by 3. This gives 9 here and this can be written as 9 upon 13. So the value of x is equal to 9 upon 13. Hence x is equal to 9 upon 13 and y is equal to minus 5 upon 13 is the required solution for the given equation. Hope you understood the elimination method. Now we will see the substitution method. Now our equations are 3x minus 5y is equal to 4. This is our first equation and 9x minus 2y is equal to 7. This is our second equation. Now we see from equation number first from equation first we get x is equal to 4 plus 5y. This implies x is equal to 4 upon 3 plus 5y upon 3 and we name it as our third equation. We further substitute the value of x in equation second. On substituting the value of x in equation second we get 9x minus 2y is equal to 7 is our second equation. Now we will place the value of x that is 9 into 4 upon 3 plus 5y upon 3 minus 2y is equal to 7. This gives 36 upon 3 plus 45 upon 3y minus 2y is equal to 7. On cancelling we get 12 plus 15y minus 2y is equal to 7 which implies 15y minus 2y is equal to 7 minus 12. This implies 15 minus 2 is 13y is equal to minus 5. This implies y is equal to minus 5 upon 13. We get the value of y is equal to minus 5 upon 13. Now we will substitute the value of y is equal to minus 5 upon 13 in equation first. 3x minus 5y is equal to 4 is our first equation. Now we will place the value of y which gives us 3x minus 5 into minus 5 upon 13 is equal to 4 which on further solving gives us 3x plus 25 upon 13 is equal to 4. This implies 3x is equal to 4 minus 25 upon 13. Here we will take the LCM 13 and this gives 13 into 4 52 minus 25 upon 13. This implies 3x is equal to 27 upon 13. This implies x is equal to 27 upon 13 into 1 upon 3. This implies x is equal to 9 upon 13. Hence x is equal to 9 upon 13 and y is equal to minus 5 upon 13 are the required solution of the given equation. Hope you understood both the methods and enjoy the session. See you and take care.