 Hello students, let's work out the following problem. It says solve the following system of linear equations. So let's now move on to the solution. The first equation given to us is 6 into ax plus by is equal to 3a plus 2b. And the second equation given to us is 6 into bx minus ay is equal to 3b minus 2a. Now the first equation can be written as 6 into ax is 6ax plus 6by is equal to 3a plus 2b. Similarly, second is written as 6bx minus 6ay is equal to 3b minus 2a. Let us name this as 1 and this as 2. Now we'll solve this system of linear equation by equating the coefficient of x or y. And here we'll equate the coefficient of y. Now to equate the coefficient of y we need to multiply equation 1 by a and equation 2 by b. So multiply equation 1 by a and 2 by b and add 1 and 2. So we'll multiply this with a and this with b. So we have 6ax into a is 6a square x plus 6by into a is 6ab y is equal to 3a into a is 3a square plus 2b into a is 2ab. Similarly, multiplying second equation by b we have 6b square x minus 6ab y is equal to 3b square minus 2ab. Now we have to add two equations. So we have 6a square x plus 6b square x but 6ab y gets cancelled with minus 6ab y. And here we have 3a square plus 3b square plus 2ab gets cancelled with minus 2ab. So again we have 6a square plus 6b square into x is equal to 3a square plus 3b square. Now taking 6 common we have 6 into a square plus b square into x is equal to 3 into a square plus b square. So we have x is equal to 3 into a square plus b square upon 6 into a square plus b square. a square plus b square gets cancelled with a square plus b square. 3 into 2 is 6 so we have x is equal to 1 by 2. Now we'll put the value of x in any one of the two equations. So now put x is equal to 1 by 2 in equation 1. Now equation 1 is 6ax x is 1 by 2 plus 6by is equal to 3a plus 2b. Now 2 into 3 is 6 so we have 3 into a is 3a plus 6by is equal to 3a plus 2b. Now 3a have the same signs on the opposite side so they get cancelled. So we have 6by is equal to 2b so this implies y is equal to 2b upon 6b so this implies y is equal to 1 by 3. Hence x is equal to 1 by 2 and y is equal to 1 by 3 is the required solution. So this completes the question and the session. Bye for now. Take care. Have a good day.