 Hello and welcome to the session. In this session we discussed the following question which says solve for x and y x plus y upon 2 equal to 4 and x upon 3 plus 2 y equal to 5. For these two equations we need to find the values for x and y. Let's proceed with its solution now. The given equations are x plus y upon 2 equal to 4. Let this be equation 1 then x upon 3 plus 2 y equal to 5. Let this be equation 2. Let's try solving both these equations by cross multiplication method. For this our first step would be to shift all the terms on the LHS so that there is 0 in the RHS. So we rewrite the equation 1 as x plus y upon 2 minus 4 equal to 0. That is we have shifted 4 from the right hand side to the left hand side and we get a 0 on the right hand side. Let this be equation 3. In the same way we rewrite the equation 2 as x upon 3 plus 2 y minus 5 equal to 0. Let this be equation 4. Here also we have shifted 5 from right hand side to the left hand side so that we get a 0 on the right hand side. Now we will solve these equations 3 and 4 by cross multiplication method. For that we write x minus y and 1 separated by equality signs like this. x upon is equal to minus y upon is equal to 1 upon. Now in the denominator of x we don't consider the coefficients of x from both these equations and we write the coefficients of y and the constant terms like this 1 upon 2 2 minus 4 minus 5. Now in the denominator of minus 5 we will not consider the coefficients of y from both these equations and we write the coefficients of x and the constant terms like this 1 upon 3 minus 4 minus 5. And for the denominator of y we won't consider the constant terms and we will write the coefficients of x and y of both these equations like this 1 upon 3 1 upon 2 and 2. Now as we have shown these arrows, these arrows indicate that these numbers are to be multiplied. So we get x upon 1 upon 2 into minus 5 that is minus 5 upon 2 minus 2 into minus 4 that is minus 8. This is equal to minus y upon 1 into minus 5 that is minus 5 minus minus 4 into 1 upon 3 that is minus 4 upon 3. And this is equal to 1 upon 1 into 2 that is 2 minus 1 upon 2 into 1 upon 3 that is 1 upon 6. We get x upon minus 5 upon 2 plus 8 is equal to minus y upon minus 5 plus 4 upon 3 is equal to 1 upon 2 minus 1 upon 6. So in solving these denominators we get x upon 11 upon 2 is equal to minus y upon minus 11 upon 3 is equal to 1 upon 11 upon 6. Now to find the value for x we will equate this first and the last expression that is x upon 11 upon 2 is equal to 1 upon 11 upon 6 that is x is equal to 11 upon 2 upon 11 upon 6 that is equal to 6 upon 2. Now 2 3 times is 6 so this is equal to 3 that is we get the value of x as 3. Now to get the value for y we equate the second and the last expression that is minus y upon minus 11 upon 3 is equal to 1 upon 11 upon 6. This gives us now this minus and minus cancels so from here we get y is equal to 11 upon 3 upon 11 upon 6 which is equal to 6 upon 3. Now 3 2 times is 6 so this is equal to 2 therefore we get y is equal to 2. So we have got the value for x and y our final answer is x equal to 3 y equal to 2. This completes the session hope you have understood the solution for this question.