 Hello friends, welcome to the session I am Malka. We are going to discuss pair of linear equations in two variables. A given equation is solve the following pair of linear equations by the elimination method and the substitution method. Our equations are x plus y equal to 5 and 2x minus 3y equal to 4. So let's start with the solution. We first consider the elimination method. So let's see elimination method. In this, our given equations are x plus y equal to 5 and 2x minus 3y equal to 4. So this is our first equation and 2x minus 3y equal to 4 is our second equation. Now, we multiply equation first by 3, we get 3x plus 3y equal to 15. Let's name this equation as our third equation. Now, we will add equation number second and equation third. We get x minus 3y equal to 4 is our second equation and 3x plus 3y equal to 15 is our third equation. Now on adding, we get 5x 3y 3y cancel out equal to 19. This implies 5x equal to 19. This implies x equal to 19 upon 5. Now, we will substitute the value of x in equation number 1. We get our equation first is x plus y equal to 5. This implies 19 upon 5 plus y equal to 5. This implies y equal to 5 minus 19 upon 5. Now, this implies on taking 5 as LCM, we get 25 minus 19 upon 5. This implies y equal to 6 upon 5. Therefore, x equal to 19 upon 5 and y equal to 6 upon 5 is the answer. Now, let's see the substitution method. Substitution method. So, in this, our given equations are x plus y equal to 5. This is our first equation and 2x minus 3y equal to 4 is our second equation. Now, from first equation, we get equal to 5 minus y. So, let this be our third equation. Now, we will substitute the value of x in equation 2. 2 into 5 minus y minus 3y equal to 4. This implies 10 minus 2y minus 3y equal to 4. This implies 10 minus 5y equal to 4. This implies minus 5y equal to 4 minus 10. This implies minus 5y equal to minus 6. This implies y equal to 6 upon 5. Now, we will use the value of y substituting value of y in equation 3rd. We get our equation 3rd is x equal to 5 minus y. This implies x equal to 5 minus 6 upon 5. This implies x equal to, on taking 5 as else, we get 25 minus 6. This implies x equal to 19 upon 5. Therefore, x equal to 19 upon 5 and y equal to 6 upon 5 is the answer. Hope you have understood the solution and enjoyed the session. Goodbye and take care.