Graphically, solve the following pair of equations
2x+y=6 and 2x-y+2=0
Find the ratio of the areas of the two triangles formed by the lines representing these equations with the X-axis and the lines with the y-axis.

Explanation

Given equations are 2x+y=6 and 2x-y+2=0
Table for equation 2x+y=6,

`{:(" "x,0,3,),(" "y,6,0,),("Points","B","A",):}`
Table for equation 2x-y+2=0,

`{:(" "x,0,-1,),(" "y,2,0,),("Points","D","C",):}`
Let `A_(1)` and `A_(2)` represent the areas of `DeltaACB` and `DeltaBDE`,respectively.

Now, `" " A_(1)`=Areaof `Delta=(1)/(2)xxAcxxPE`
`" " =(1)/(2)xx4xx4=8`
and `" " A_(2)`= Area of `DeltaBDE=(1)/(2)xxBDxxQE`
`" " =(1)/(2)xx4xx1=2`
`" " :. A_(1) : A_(2)= 8 : 2= 4 : 1`
Hence, the pair of equations intersect graphically at point E(1, 4), i.e., x=1 and y=4.