Draw the graph of the pair of equations 2x+y=4 and 2x-y=4. Write the vertices of the triangle formed by these lines and the y-axis, find the area of this triangle?

Explanation

The given pair of linear equations
Table for line 2x+y=4,
`{:(" "x,0,2,),(y=4-2x,4,0,),(" ""Points",A,B,):}`
and table for line 2x-y=4,
`{:(" "x,0,2,),(y=2x-4,-4,0,),(" ""Points",C,B,):}`

Graphical representation of both lines.
Here, both lines and Y-axis form a `DeltaABC`.
Hence, the vertices of a `DeltaABC` are A(0,4) B(2,0) and C(0, -4).
`:. " "` Required area of `DeltaABC=2xx`Area of `DeltaAOB`
`" " =2xx(1)/(2)xx4xx2=8`sq units
Hence, the required area of the triangle is 8 sq units.