The area (in sq. units) of the triangle formed by the graphs of 8x + 3y = 24, 2x + 8 = y and the x-axis is:

Solution (By Examveda Team)

$$\eqalign{ & {\text{At }}x{\text{ - axis}},\,y = 0 \cr & 8x + 3y = 24 \cr & x = 3 \cr & 2x + 8 = y \cr & x = - 4 \cr & \,\,\,8x + 3y = 24 \to \left( {\text{i}} \right) \cr & \,\,\,8x - 4y = 32 \to \left( {{\text{ii}}} \right) \cr & \underline {\, - \,\,\,\,\, + \,\,\,\,\,\,\,\,\, + \,\,\,\,\,\,\,\,} \cr & 7y = 56 \cr & y = 8 \cr & {\text{Area}} = \frac{1}{2} \times {\text{base}} \times {\text{height}} \cr & = \frac{1}{2} \times 7 \times 8 \cr & = 28 \cr} $$