What is the area (in unit squares) of the region enclosed by the graphs of the equations 2x - 3y + 6 = 0, 4x + y = 16 and y = 0?

Solution (By Examveda Team)

2x - 3y + 6 = 0
y = 0
⇒ 2x - 3 × 0 = -6
2x = -6
x = -3
y = 0
y = 0 ⇒ 4x + 0 = 16
x = 4 ; y = 0
$$\eqalign{ & 2x - 3y = - 6\,\,\, * 2 \cr & \underline {4x + y = 16\,\,} \,\,\,\,\, * 1 \cr} $$
4x - 6y = -12 . . . . . . (i)
4x + y = 16 . . . . . . (ii)
Solve equation (i) and (ii)
y = 4 ; x = 3

$$\Delta {\text{ABC}} = \frac{1}{2} \times \left( {4 + 3} \right) \times 4 = 14$$