 Hello friends, welcome to the session. I am Malka. We are going to discuss pair of linear equations in two variables We have to solve the following pair of linear equations for the elimination method and the substitution method Now our given equations are x upon 2 plus 2 by upon 3 equal to minus 1 and x minus y upon 3 equal to 3 Now let's start with the solution by elimination method. Now we are given with the equations x upon 2 plus 2 by upon 3 equal to minus 1 and x minus y upon 3 equal to 3 Multiply equations second by 2 We get 2x minus 2y upon 3 equal to 6. Now let this be our third equation. Now we will add equation number 1 3 we get x upon 2 plus 2y upon 3 equal to minus 1 and second equation is 2x minus 2y upon 3 equal to 6. On adding these two equations we get x upon 2 plus 2x and 2y upon 3 will cancel out with 2y upon 3 and this is equal to 5 This can be written as x upon 2 plus 2x equal to 5 this implies x plus 4x upon 2 equal to 5 on cross multiplying we get 5x equal to 10 this implies x equal to 2 Now We'll substitute the value of x equal to 2 in equation second. My question second is x minus y upon 3 equal to 3. Now we'll substitute the value of x equal to 2 in this equation. This will give us 2 minus y upon 3 equal to 3 this implies minus y upon 3 equal to 3 minus 2 this implies minus y upon 3 equal to 1 this implies y equal to minus 3 Thus x equal to 2 and y equal to minus 3 Now we'll see the substitution method. Now we'll see the substitution method our equations are x upon 2 plus 2y upon 3 equal to minus 1. This is our first equation and x minus y upon 3 equal to 3 This is our second equation now From equations second we get x equal to 3 plus y upon 3 Let this be our third equation. Now we'll substitute the value of x in equation first we get 3 plus y upon 3 into 1 by 2 plus 2y upon 3 equal to minus 1 this implies 9 plus y upon 3 into 1 by 2 plus 2y upon 3 equal to minus 1 this implies 9 plus y upon 6 plus 2y upon 3 equal to minus 1 this implies on multiplying both the sides by 6 we get 9 plus y plus 2y into 2 equal to minus 6 this implies 5y equal to minus 6 minus 9 this implies y equal to minus 15 upon 5 this implies y equal to minus 3 Now on substituting the value of y equal to minus 3 in equation third we get on Substituting the value of y in equation third which is x equal to 3 plus y upon 3 we get x equal to 3 plus minus 3 upon 3 this implies x equal to 3 minus 3 upon 3 this implies x equal to 3 minus 1 this implies x equal to 2 hence x equal to 2 and y equal to minus 3 is the required answer Hope you understood the solution and enjoyed the session goodbye and take care