 Hello and welcome to the session that is discussed the following question. It says solve for x and y So let's now move on to the solution given equations are 4 upon x plus 5 y is equal to 7 and 3 upon x plus 4 y is equal to 5 now we'll solve the system of equations by equating the coefficient of x or y here we'll equate the coefficient of y so to equate the coefficient of y multiply Equation 1 by 4 and 2 by 5 and subtract equation 2 from 1 so now we'll multiply equation 1 by 4 and 2 by 5 so we'll have 4 by x into 4 is 16 by x plus 4 y 5 y into 4 is 20 y is equal to 7 then 3 by x into 5 is 15 by x plus 4 y into 5 is 20 y is equal to 5 into 5 is 25 and here also 7 into 4 is 28 So we need to write 28 now we have to subtract equation 2 from equation 1 After multiplying equation 1 by 4 and 2 by 5 So as we know that whenever we subtract sign changes now 16 by x minus 15 by x is 1 by x Taking LCM we'll have 16 by 16 minus 15 upon x so it is 1 by x plus 20 y gets cancelled with minus 20 y and 28 minus 25 is 3 So this implies 1 by x is equal to 3 So this implies x is equal to 1 by 3 right now we'll put x is equal to 1 by 3 in any one of the two equations equation 1 or equation 2 So we'll put it in equation 1 To get the value of y now equation 1 was 4 upon x so it is 4 upon x x is 1 by 3 plus 5 y is Equal to 7 Now again this implies 4 upon 1 upon 3 is 4 into 3 by 1 Plus 5 y is equal to 7 and this is equal to 12 plus 5 y is equal to 7 This implies 5 y is equal to 7 minus 12 So this implies 5 y is equal to minus 5 Dividing both sides by 5 we have Y is equal to minus 1 so we have x is equal to 1 by 3 and Y is equal to minus 1 the solution of the given system of equations Do take care of all your calculation while solving the question well for now take care. Have a good day