To solve the given system of equations using cross multiplication, we need to follow the steps outlined below:

Step 1: Expand the expressions
- Expand 2(ax - by) as 2ax - 2by
- Expand 2(bx + ay) as 2bx + 2ay

Step 2: Rewrite the equations
- 2ax - 2by = 4b (Equation 1)
- 2bx + 2ay = b - 4a (Equation 2)

Step 3: Cross multiply
We will cross multiply the terms to eliminate the denominators and simplify the equations.

- For Equation 1:
Multiply both sides by (a - b) to get:
(2ax - 2by)(a - b) = 4b(a - b)
This simplifies to: 2ax(a - b) - 2by(a - b) = 4b(a - b)

- For Equation 2:
Multiply both sides by (b + a) to get:
(2bx + 2ay)(b + a) = (b - 4a)(b + a)
This simplifies to: 2bx(b + a) + 2ay(b + a) = (b - 4a)(b + a)

Step 4: Simplify the equations
After expanding and simplifying the equations obtained from cross multiplication, we can simplify them further.

- For Equation 1:
2ax(a - b) - 2by(a - b) = 4b(a - b)
Simplifying this equation yields: 2a^2x - 2abx - 2aby + 2b^2y = 4ab - 4b^2

- For Equation 2:
2bx(b + a) + 2ay(b + a) = (b - 4a)(b + a)
Simplifying this equation yields: 2b^2x + 2abx + 2aby + 2a^2y = b^2 - 4ab + ab - 4a^2
Simplifying further: 2b^2x + 2abx + 2aby + 2a^2y = b^2 - 3ab - 4a^2

Step 5: Rearrange the equations
Rearranging the equations obtained in the previous step will help us solve for the variables.

- Equation 1: 2a^2x - 2abx - 2aby + 2b^2y = 4ab - 4b^2
Rearranging gives: 2a^2x - 2abx - 2aby + 2b^2y - 4ab + 4b^2 = 0

- Equation 2: 2b^2x + 2abx + 2aby + 2a^2y = b^2 - 3ab - 4a^2
Rearranging gives: 2b^2x + 2abx + 2aby + 2a^2y - b^2 + 3ab + 4a^2 = 0

Step 6: Solve for the