 Hello and welcome to the session. In this session we discussed the following question which says solve for x and y 37x plus 41y is equal to 70, 41x plus 37y is equal to 86. So we have given these two equations and we need to find the value for x and y. Let's see its solution now. We have the equation 37x plus 41y equal to 70. Let this be equation then 41x plus 37y is equal to 86. Let this be equation 2. Now adding equations 1 and 2 we get 37x plus 41y plus 41x plus 37y is equal to 70 plus 86. This gives us 78x plus 78y is equal to 156. Now we take 78 common here. So 78 is whole into x plus y is equal to 156. This gives us x plus y is equal to 156 upon 78 and 78 2 times is 156. Therefore we get x plus y is equal to 2. We take this as equation 3. Then we subtract equation 1 from equation 2. So subtracting 1 from equation 2 we get 41x plus 37y minus 37x plus 41y is equal to 86 minus 70. That is we have 41x plus 37y minus 37x minus 41y is equal to 16. This further gives us 41x minus 37x is 4x plus 37y minus 41y is minus 4y. This is equal to 16. We take common 4. Inside we have x minus y equal to 16. This gives us x minus y is equal to 16 upon 4. Now 4 times is 16. Therefore we have x minus y is equal to 4. That is the equation 4. Now we have 2 equations. Equation 3 that is x plus y equal to 2 and equation 4 x minus y equal to 4. So adding equations 3 and 4 we get x plus y plus x minus y is equal to 2 plus 4. That is we have now this y and minus y cancels. So this gives us 2x is equal to 6 which means x is equal to 6 upon 2. Now 2 3 times is 6. So we get x is equal to 3. So we have now got the value for x as 3. Now substituting x equal to 3 in equation 3 we get x plus y equal to 2 is the third equation. So on putting x equal to 3 we would get 3 plus y equal to 2. This gives us y is equal to 2 minus 3 which is equal to minus 1. Therefore y is equal to minus 1 is the value for y. So our final answer is x equal to 3 and y equal to minus 1. So this completes the session. Hope you have understood the solution for this question.