Question

Graphically, solve the following pair of equations:
$2x+y=6;2x-y+2=0$
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.

Answer 1

According to the question, the graph of the line would be;

On solving, we get point as $(1,4)$.

$ar\left(△DOC\right)=\frac{1}{2}\left(OD\right)\left(OC\right)=\frac{1}{2}\times 1\times 2=1sq.units$

$ar\left(△AOB\right)=\frac{1}{2}\left(OB\right)\left(OA\right)=\frac{1}{2}\times 3\times 6=9sq.units$

$\therefore$ Ratio of areas = 1:9