1. Solve the simultaneous equations: Given the system: $$\begin{cases} 2x + 3y = 12 \\ x - y = 3 \end{cases}$$ Step 1: From the second equation, express $x$ in terms of $y$: $$x = y + 3$$ Step 2: Substitute $x = y + 3$ into the first equation: $$2(y + 3) + 3y = 12$$ Step 3: Simplify and solve for $y$: $$2y + 6 + 3y = 12$$ $$5y + 6 = 12$$ $$5y = 6$$ $$y = \frac{6}{5} = 1.2$$ Step 4: Substitute $y = 1.2$ back into $x = y + 3$: $$x = 1.2 + 3 = 4.2$$ 2. Simplify the algebraic fraction: $$\frac{3x^2 - 12}{6x}$$ Step 1: Factor numerator: $$3x^2 - 12 = 3(x^2 - 4) = 3(x - 2)(x + 2)$$ Step 2: Write fraction: $$\frac{3(x - 2)(x + 2)}{6x}$$ Step 3: Simplify coefficients: $$\frac{3}{6} = \frac{1}{2}$$ Step 4: Final simplified form: $$\frac{(x - 2)(x + 2)}{2x}$$ 3. Find the sum of interior angles of a polygon with 8 sides: Formula: $$\text{Sum} = (n - 2) \times 180$$ where $n=8$ $$\text{Sum} = (8 - 2) \times 180 = 6 \times 180 = 1080$$ degrees 4. Simplify the surd: $$\sqrt{50} + \sqrt{18}$$ Step 1: Simplify each surd: $$\sqrt{50} = \sqrt{25 \times 2} = 5\sqrt{2}$$ $$\sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2}$$ Step 2: Add: $$5\sqrt{2} + 3\sqrt{2} = 8\sqrt{2}$$ 5. Calculate the area of a rectangle with length 7 cm and width 5 cm: Formula: $$\text{Area} = \text{length} \times \text{width}$$ $$= 7 \times 5 = 35$$ cm² 6. Find the perimeter of a triangle with sides 6 cm, 8 cm, and 10 cm: Formula: $$\text{Perimeter} = 6 + 8 + 10 = 24$$ cm 7. Calculate the volume of a cube with side length 4 cm: Formula: $$\text{Volume} = \text{side}^3 = 4^3 = 64$$ cm³