 Hello and welcome to the session. In this session we discussed the following question which says solve x plus y equal to 7 and 3x minus 2y equal to 11. Let's proceed with the solution now. We are given simultaneous linear equations x plus y equal to 7 and 3x minus 2y equal to 11. Let this be equation 1 and this be equation 2. Now as you can see, in these two equations the coefficients of the variables in the two equations are different. Now we will solve these two equations for the values of x and y. We solve these equations using the elimination method in which we make the coefficients of one of the variables in the two equations equal by multiplying both sides of the equation by suitable numbers. So here we will make the coefficients of the variable x equal in these two equations. As you can see in the second equation the coefficient of the variable x is 3 and in the first equation the coefficient of the variable x is 1. So we will make the coefficient of x in the equation 1 as 3. This can be done by multiplying the equation 1 by the number 3 on both sides. So first of all multiplying equation 1 by 3 we get 3 multiplied by x plus y equal to 3 multiplied by 7. This gives us 3x plus 3y is equal to 21. So we have rewritten equation 1 as this that is 3x plus 3y is equal to 21. Now our second equation was 3x minus 2y is equal to 11. Now let this be equation 3 and this is equation 2 itself. Now we can solve these two equations to get the values of x and y. Since we have got the coefficients of the variable x same in both the equations so now we would subtract equation 2 from equation 3. So subtracting equation 2 from equation 3 we get 3x plus 3y minus 3x minus 2y the whole is equal to 21 minus 11. Thus further we get 3x plus 3y minus 3x plus 2y is equal to 10 or we have 3x cancels with minus 3x and now 3y plus 2y is 5y is equal to 10. Now to get the value for y we divide both sides by 5 and now 5 cancels with 5 and 5 2 times its 10 so we get y as 2 thus we get the value for y as 2. Now to get the value for x we would substitute the value of y in either of the two equations 2 and 3 thus substituting y equal to 2 in equation 3 we get that is in this equation we would put y as 2 so we have 3x plus 3 multiplied by 2 is equal to 21. This means we have 3x plus 6 is equal to 21 or 3x is equal to 21 minus 6 so now we have 3x is equal to 15. To get the value for x we divide both sides by 3 here 3 cancels with 3 and 3 5 times is 15 therefore we get x is equal to 5 so for the given simultaneous linear equations we get the value of x as 5 and value of y as 2 thus our final answer is x equal to 5 and y equal to 2. This completes the session hope you have understood the solution of this question.