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

Answer: Option A

Solution

Answer: Option A

Solution:

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