 Hello friends, welcome to the session. I am Alka. I am going to help you solve the 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 question is 3x plus 4y is equal to 10 and 2x minus 2y is equal to 2. So, let's start with a solution. First, we will see the elimination method. Now, our equation 3x plus 4y is equal to 10 and let us name it as first and our second equation is 2x minus 2y is equal to 2. This is our second equation. Now, what we can do is we have to make the coefficient of any of the variables same. For this, let us multiply our equation second by 2. We will multiply equation second by 2 and get 4x minus 4y is equal to 4. So, this is our third equation. Now, we see that our equation number 1 and equation number 3 share the same coefficient of variable y. So, on adding, if we add these two equation, equation number 1 and equation number 3, adding equation 1 and 3, we get 3x plus 4y is equal to 10 and 4x minus 4y is equal to 4. We are adding these two equations. This gives us 7x. This will get cancelled out is equal to 14. This means, this implies that the value of x is equal to 14 upon 7 which can be written as x is equal to 2. Now, on further substituting the value of x is equal to 2 in equation first, on substituting the value of x is equal to 2 in equation first, we get our equation first is 3x plus 4y is equal to 10. Now, in place of x, we will write 2. This gives 4y is equal to 10. This implies 6 plus 4y is equal to 10. Again 4y is equal to 10 minus 6. This gives y is equal to 4y4 equal to 1. Therefore, y is equal to 1. Hence, x is equal to 2 and y is equal to 1 are the required values of the variables x and y by elimination method. Hope you understood the elimination method. Now, by substitution method, we see our given equations are 3x plus 4y is equal to 10 and second equation is 2x minus 2y is equal to 2. Let us name this as first equation and this as second. We see from equation second, we get the value of x which is equal to x is equal to 2 plus 2y. This can be written as x is equal to 2 upon 2 plus 2y upon 2. This implies x is equal to 1 plus y. So, this is the value of y which will substitute in equation number 1. Now, we will substitute the value of x is equal to 1 plus y in equation first. Our equation first is 3x plus 4y is equal to 10. Now, we will place the value of x which is 1 plus y. This gives us on opening the bracket, we see 3 plus 3y plus 4y is equal to 10. This implies 7y is equal to 10 minus 3. This implies y is equal to 7 upon 7 is equal to 1. Therefore, value of y is equal to 1. Now, we will substitute the value of y is equal to 1 in equation number 3. On substituting the value of y is equal to 1 in equation number 3 which is x is equal to 1 plus y, we get x is equal to 1 plus 1. This implies x is equal to 2. Hence, x is equal to 2 and y is equal to 1 is the required solution of the given equation. Hope you understood both the method and enjoyed the session. See you and take care.