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.

Solution

## $$\begin{array}{l} 2x+y=6 \\ put\, \, x=0 \\ y=6 \\ put\, x=1 \\ y=4 \\ put\, \, x=2 \\ y=2 \\ and\, \, 2x-y+2=0 \\ put\, \, y=0 \\ x=1 \\ put\, \, x=0 \\ y=2 \\ put\, x=2 \\ y=6 \\ and\, \, x-y=0 \\ x=0,\, \, y=0 \\ x=1,y=1 \\ x=2,\, y=2 \end{array}$$Area of bounded region$$\begin{array}{l} \frac { 1 }{ 2 } \left[ { 1\left( { -2-2 } \right) -2\left( { 2-4 } \right) +2\left( { 4+2 } \right) } \right] \\ \frac { 1 }{ 2 } \left[ { -4+4+12 } \right] \\ 6\, \, sq.\, unit \end{array}$$Mathematics

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