Question

Draw the graph of $2x+y=6$ and $2x-y+2=0$. Shade the region bounded by these lines and $x-y$. Find the area of the shaded region.

Answer 1

$\begin{array}{c}2x+y=6\\ putx=0\\ y=6\\ putx=1\\ y=4\\ putx=2\\ y=2\\ and2x-y+2=0\\ puty=0\\ x=1\\ putx=0\\ y=2\\ putx=2\\ y=6\\ andx-y=0\\ x=0,y=0\\ x=1,y=1\\ x=2,y=2\end{array}$

Area of bounded region

$\begin{array}{c}\frac{1}{2}\left[1\left(-2-2\right)-2\left(2-4\right)+2\left(4+2\right)\right]\\ \frac{1}{2}\left[-4+4+12\right]\\ 6sq.unit\end{array}$