 Hello students let's work out the following problem it says solve for x and y so let's now start the solution first equation given to us is a x upon b minus by upon a is equal to a plus b let us first simplify this equation and we take ncm here ncm would be ab and in the numerator will have a square x minus b square y is equal to a plus b and this implies a square x minus b square y is equal to ab into a plus b and this again implies a square x minus b square y is equal to ab into a is a square b ab into b is ab square let's name this as 1 and the second equation given to us is a x minus b y is equal to 2ab let's name this as 2 now we will solve a system of equation by equating the coefficient of x or y and here we will be equating the coefficient of x for that you see that we need to multiply second equation by a because in the first equation the coefficient of x is a square and in the second equation the coefficient of x is a so we need to multiply equation 2 by a so multiply equation 2 by a and the first equation is a square x minus b square y is equal to ab into this a square b plus ab square now multiplying equation 2 by a we have a square x minus ab y is equal to 2 a square b now we have to subtract equation 2 from equation 1 the sign changes now plus a square x gets cancelled with minus a square x and this becomes ab minus b square y is equal to a square b minus ab square plus ab square minus 2 a square b so this implies b into a minus b y taking b common is equal to ab square a square b minus 2 a square b is minus a square b and this again implies b into a minus b y is equal to taking ab common we have ab into b minus a and this implies y is equal to ab into b minus a upon b into a minus b and thus again implies b gets cancelled with b we have y is equal to taking minus common we have minus a into a minus b upon a minus b and now a minus b gets cancelled with a minus b and we have y is equal to minus a now we will put y is equal to minus a in any one of the two equations the equation one or equation two to get the value of x so we will put y is equal to minus a in equation 2 from equation 2 we have a x minus b y and here y is minus a is equal to 2 ab so this implies a x plus ab is equal to 2 ab and this implies a x is equal to 2 ab minus ab and this implies a x is equal to ab and this implies x is equal to ab upon a and this again implies x is equal to b hence equal to b and y is equal to minus a is the solution the given equations the system gets a question and the session why for now take care