 Hello friends, welcome to the session I am Alka and we are going to discuss matrices. We have to find the value of x and y if 2x plus 3y equal to matrix 2,3,4,0 and 3x plus 2y equal to matrix 2 minus 2 minus 1 and 5. So let's start with the solution. We are given with two equations 2x plus 3y equal to 2,3,4,0 matrix which we name as our first equation and 3x plus 2y equal to 2 minus 2 minus 1,5 matrix which we name as our second equation. Now we will multiply our equation first by 3 and on multiplying equation second by 2 we get 6x plus 9y equal to matrix 6,9,12,0 and 6x plus 4y equal to matrix 4 minus 4 minus 2,10. Now we name it as our third equation and this as our fourth equation. Now on subtracting equation fourth from third we get 9y minus 4y equal to 6,9,12,0 minus 4 minus 4 minus 2,10. Or this can be written as 5y equal to 6,9,12,0 plus minus 4,4,2, minus 10. This is equal to 6 minus 4,9 plus 4,12 plus 2,0 minus 10. This is equal to 2,13,14 and minus 10. This implies y equal to one-fifth of matrix 2,13. This implies y equal to 2 by 5,13 by 5,14 by 5 and minus 2. Now we have to find the value of x. So we will substitute this value of y in equation first or second. Now we will substitute this value in equation first. We get our equation first is 2x plus 3y equal to matrix 2,3,4,0. Now we will place the value of y. This gives us 2x plus 3 into value of y. That is 2 by 5,13 by 5,14 by 5 and minus 2 equal to matrix 2,3,4,0. This is equal to 2x plus matrix 6 by 5,39 by 5,42 by 5, minus 6 equal to matrix 2,3,4,0. This implies 2x equal to 2,3,4,0 matrix minus the second matrix which is 6 by 5,42 by 5, 39 by 5 and minus 6. This implies 2x equal to 2 minus 6 by 5,3 minus 39 by 5,4 minus 42.5 and 0 minus 6 which is plus 6 because minus minus will get plus. This implies x equal to 2 by 5 minus 12 by 5 minus 11 by 5 and 3. Thus, x equal to matrix 2 by 5 minus 12 by 5 minus 11 by 5,3 and y equal to matrix 2 by 5,13 by 5,14 by 5 minus 2 which is the required answer. Hope you understood the solution and enjoyed the session. Goodbye and take care.