 Hello and welcome to the session, I am Deepika here. Let's discuss a question. Solve system of linear equations using matrix method 4x-3y is equal to 3, 3x-5y is equal to 7. Let's start the solution. The given system of equations can be written in the form x is equal to b where a is equal to 4-3, 3-5, x is equal to x5 and b is equal to 3, 7. Now determinant a is equal to minus 20 plus 9 which is equal to minus 11 that is not equal to 0. This implies a is non-singular hence its inverse exists. So we will first find out the inverse. Now adjoint a is equal to 5, 4 and this is 3 minus 3. Therefore a inverse is equal to 1 over determinant a into adjoint this implies a inverse is equal to 1 over minus 11 into minus 5 minus 3, 3, 4. Now ax is equal to b implies a inverse ax is equal to a inverse b by pre-multiplying both sides by a inverse. This implies ix is equal to a inverse b this implies x is equal to now a inverse is minus 1 over 11 into minus 5 minus 3, 3, 4 into b. b is a 3, 7 is equal to minus 1 by 11 into minus 5 into 3 minus 15 plus 3 into 7, 21 here minus 3 into 3 minus 9 plus 28. This is equal to minus 1 by 11 and 19. This implies xy is equal to minus 6 by 11 and minus 19 by 11. So by equating the corresponding coefficients we get x is equal to minus 6 by 11 and y is equal to minus 19 by 11. So we have solved the above system of equations using matrix method and our answer is x is equal to minus 6 by 11 and y is equal to minus 19 by 11. I hope question is clear to you. Bye and have a nice day.