Solve the following systems of equations and find the perimeter of the rectangle.

Here are the solutions to the problems:

Question 4a:
We need to solve the system of equations using the elimination method:

$$\frac{2}{5}x - \frac{1}{10}y = 3 \quad (1)$$ $$\frac{2}{3}x + \frac{2}{3}y = 0 \quad (2)$$

Step 1: Clear the denominators in both equations.
Multiply equation (1) by 10:

$$10 \left( \frac{2}{5}x - \frac{1}{10}y \right) = 10(3)$$ $$4x - y = 30 \quad (3)$$

Multiply equation (2) by 3:

$$3 \left( \frac{2}{3}x + \frac{2}{3}y \right) = 3(0)$$ $$2x + 2y = 0$$

Divide by 2:

$$x + y = 0 \quad (4)$$

Step 2: Use the elimination method on the new system of equations (3) and (4).
Add equation (3) and equation (4) to eliminate $y$:

$$(4x - y) + (x + y) = 30 + 0$$ $$5x = 30$$

Step 3: Solve for $x$.

$$x = \frac{30}{5}$$ $$x = 6$$

Step 4: Substitute the value of $x$ into equation (4) to find $y$.

$$6 + y = 0$$ $$y = -6$$

The solution is $\boxed{x=6, y=-6}$.