Graphical solution of linear equations and triangle area

For $2x - y = 1$:

• $x = 0 \implies y = -1 \implies (0, -1)$
• $y = 0 \implies x = 0.5 \implies (0.5, 0)$
• $x = 2 \implies y = 3 \implies (2, 3)$

For $3x + 2y = 12$:

• $x = 0 \implies y = 6 \implies (0, 6)$
• $y = 0 \implies x = 4 \implies (4, 0)$
• $x = 2 \implies y = 3 \implies (2, 3)$

Intersection point of the two lines is $A(2, 3)$. Intersections with x-axis: Line 1 at $B(0.5, 0)$ and Line 2 at $C(4, 0)$. Vertices of the triangle formed with x-axis are $(2, 3)$, $(0.5, 0)$, and $(4, 0)$. Base length $= 4 - 0.5 = 3.5\text{ units}$. Height $= y$-coordinate of intersection $= 3\text{ units}$. Area $= \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 3.5 \times 3 = 5.25\text{ sq units}$.