Question

Solve each of the following systems of equations by the method of cross-multiplication 

`x/a = y/b`

`ax + by = a^2 + b^2`

Answer 1

`x/a = y/b`

``ax + by = a^2 + b^2`

Here `a_1 = 1/a, b_1 = (-1)/b, c_1 = 0`

`a_2 = a, b_2 = b,c_2 = -(a^2 + b^2)`

By cross multiplication, we get

`x/(-1/b(-(a^2 + b^2))-b(0)) = (-y)/(1/a(-(a^2 + b^2))-a(0)) = 1/(1/a (b) - a xx ((-1)/b))`

`x/((a^2 + b^2)/b) = y/((a^2 + b^2)/a) = 1/(b/a + a/b)`

`x = ((a^2 + b^2)/b)/(b/a + a/b) = ((a^2 +b^2)/b)/((b^2 + a^2)/(ab)) = a`

`y = ((a^2 + b^2)/a)/(b/a + a/b) = ((a^2 + b^2)/b)/((b^2+a^2)/(ab)) = b`

Solution is (a, b)