 Hello and welcome to the session. In this session we discussed the following question which says solve for x and y, 6 into mx plus ny is equal to 3m plus 2n, 6 into nx minus ny is equal to 3n minus 2n. So we are given two equations we need to solve for x and y that is we need to find the values for x and y. Let's move on to the solution. The given equations are 6 into mx plus ny is equal to 3m plus 2n. Let this be equation one then 6 into nx minus ny is equal to 3n minus 2m. Let this be equation two. Now we can rewrite equation one as 6mx plus 6n y is equal to 3m plus 2n then in the same way we can rewrite the equation two as 6n x minus 6m y is equal to 3n minus 2n. Let this be equation three and this be equation four. Now let's multiply equation three by m and we get 6m square into x plus 6mn into y is equal to 3m square plus 2mn. Let this be equation five. Then we multiply equation four by n and we get 6n square into x minus 6mn into y is equal to 3n square minus 2mn. Let this be equation six. Now adding equations five and six we get 6n square plus 6n square this whole into x plus 6mn into y minus 6mn into y and this is equal to 3m square plus 3n square plus 2mn minus 2mn. Now 6mn y minus 6mn y cancels then 2mn minus 2mn cancels so we get 6n square plus 6mn square this whole into x is equal to 3mn square plus n square that is x is equal to 3mn square plus n square this whole upon 6mn square plus n square. Now n square plus n square cancels and three two times is 6 so this is equal to one upon two. We have the value of x as one upon two. Now we substitute x equal to one upon two in equation three and substituting x equal to one upon two in equation three we get. Now this is equation three so on substituting x equal to one upon two this would give us 6m into one upon two plus 6n y is equal to 3m plus 2n. Now two three times is six so we have 3m plus 6n y is equal to 3m plus 2n. This further gives us 6n y is equal to 3m plus 2n minus 3m. Now 3mn minus 3m cancels and we have y is equal to 2n upon 6n. This nn gets cancelled and two three times is six therefore we get y is equal to one upon three. So on solving the given two equations we get x equal to one upon two and y equal to one upon three. This is our final answer. This completes the session. Hope you have understood the solution for this question.