 Hello and welcome to the session. The given question says, solve the following system of linear equations and here we are given two equations. We have to find the value of x and y. Let's begin with the solution. Now the first equation can be written as 2Ax minus 2By plus A plus 4B is equal to 0. Let this be equation number one and the second equation can be written as 2Bx plus 2Ay plus B minus 4A is equal to 0. Let this be equation number two. Here we shall solve these two equations for x and y by equating the coefficient so multiplying equation one by A and 2 by B. On multiplying equation one by A here we have 2A square x minus 2ABy plus A square plus 4AB is equal to 0. Let this be equation number three and on multiplying equation two by B we have 2B square x plus 2ABy plus B square minus 4AB is equal to 0. Let this be equation number four. Now we shall be adding both these equations to find the value of x first. So on adding here we have here two times of A square x plus two times of B square x. Here these two terms cancel out since they are like terms with opposite signs and these two terms have A square plus B square and this is equal to 0 and this we get on adding third equation with the fourth equation. This further implies that two times of A square plus B square into x is equal to minus of A square plus B square or x is equal to minus of A square plus B square divided by two times of A square plus B square canceling the common term from the numerator and denominator we have minus half therefore x is equal to minus half. Now next we shall substitute the value of x in the given equation. So substituting x is equal to minus half in equation number one. Now first let us write down equation one which is given to us. This two into A x minus BY plus A plus 4B is equal to 0. Now replacing x by minus half we have two times of inside the bracket minus A divided by two minus BY is equal to taking this term on the right hand side we have minus of A plus 4B or we have from here minus A minus two times of BY is equal to minus A minus 4B. Now minus A cancels out with minus A. This further implies that Y is equal to minus 4B divided by minus 2B which gives the value of Y as two. Therefore Y is equal to two. Hence on solving the given equation for x and y we have x is equal to minus half and Y is equal to two. So this completes the session. Hope you have understood it well. Bye and take care.