The figure shows a circuit having eight resistances of 1 $$\Omega$$ each, labelled $$R_1$$ to $$R_8$$, and two ideal batteries with voltages $$\varepsilon_1 = 12$$ V and $$\varepsilon_2 = 6$$ V.

Which of the following statement(s) is(are) correct?

For loop 1:

$$-\frac{1}{2}x - \frac{1}{2}(x + y) - x + 6 = 0$$

$$\Rightarrow -2x - \frac{y}{2} = -6$$

$$\Rightarrow -4x - y = -12$$

$$\Rightarrow 4x + y = 12 \dots \dots \dots (1)$$

For loop 2:

$$\frac{1}{2}y + 1y + 12 + \frac{1}{2}(x + y) = 0$$

$$\Rightarrow \frac{3}{2}y + \frac{y}{2} + \frac{x}{2} = -12$$

$$\Rightarrow 2y + \frac{x}{2} = -12$$

$$\Rightarrow 4y + x = -24$$

$$\Rightarrow 4y + x - 16x - 4y = -24 - 48$$

$$\Rightarrow -15x = -72$$ $$\Rightarrow x = \frac{72}{15}$$

$$\Rightarrow 4\left(\frac{72}{15}\right) + y = 12$$

$$\Rightarrow y = 12 - \frac{288}{15}$$

$$= \frac{180 - 288}{15}$$

$$= \frac{-108}{15} = -7.2\text{ A}$$

Current in $$R_1 = 7.2\text{ A}$$

Current in $$R_2 = \frac{x+y}{2} = \left(\frac{72}{15} - \frac{108}{15}\right) \frac{1}{2}$$

$$= \frac{1}{2}\left(\frac{-36}{15}\right) = \frac{-2.4}{2}\text{ A}$$ $$= -1.2\text{ A}$$

Current in $$R_3 = x = 4.8\text{ A}$$

Current in $$R_4 = \frac{1}{2}x = 2.4\text{ A}$$