Question

You are given the following system of equations:

c=ax + by

$f=dx+ey$

Design a system which calculates x and y given a, b, c, d, e, and f. You may use any architecture of your choosing. You may also assume that n-bit dividers are available.

Answer 1

We have given the following system of equations ax + by = c rightarrow equation (1) dx + ey = f rightarrow equation (2) so we have to calculate x and y by using the a, b, c, d, e, f .we can use any of the architecture written the equations in the matrix form ax + by = c dx + e y = f [a d e] times [x y] = [c y] so now from the above matrix form we can calculate (x, y) values [a b d e] [x y] = [c f] [x y] = [a d b e] [c f] [x y] = [a d b e]^-1[c f] calculating the inverse matrix by using determinant formula.[x y] = 1/ ae- db [e -d -b a] [c f] = 1/ ae- db [ec -cd - bf + af] [x y] = [ec-bf/ ea-db af- cd/ ae-db]