 Hello students let's work out the following problem it says solve for x and y so let's now move on to the solution the given two equations are 47 x plus 31 y is equal to 63 and 31 x plus 47 y is equal to 15 let's name this as 1 and this as 2 now we'll solve the system of equation by equating the coefficient of x or y and here we'll be equating the coefficient of y so to equate the coefficient of y we'll multiply equation 1 by 47 and 2 by 31 31 and also 2 from 1 multiplying equation 1 by 47 gives us 47 into 47 is 2200 9 x plus 31 y into 47 is 1457 y is equal to 63 into 47 is 2961 now multiplying equation 2 y 31 31 x into 31 is 961 x plus 47 y into 31 is 1457 y is equal to 15 into 31 is 465 now we have to subtract equation 2 from equation 1 and we know that whenever we subtract sign changes now 2200 9 x minus 961 x is equal to 1248 x 1457 y gets cancelled with minus 1457 y 2961 minus 465 is 2496 so this implies x is equal to 2496 upon 1248 now dividing 2496 by 1248 gives us x is equal to 2 now we'll put the value of x in any one of the two equations either equation 1 or equation 2 to get the value of y so we'll put x is equal to 2 in equation 1 so we have from 1 47 x is 47 into 2 plus 31 y is equal to 63 now 47 into 2 is 94 plus 31 y is equal to 63 and this implies 31 y is equal to 63 minus 94 and this implies 31 y is equal to minus 31 63 minus 94 is minus 31 and this implies y is equal to minus 1 hence is equal to 2 and y is equal to minus 1 is the solution of the given equations please the session bye for now take care have a very nice day