Question

Solve the following pair of linear equation graphically and shade the region bounded by these lines and x - axis; also find the area of the shaded region.
$2x+y=6;2x-y=0$

Answer 1

The given equation
is $2x+y=6$ and $2x-y=0$
Now, let us find atleast two solutions of each of the above equations, as shown
in the following tables.
Table for $2x+y=6$ or $y=6-2x$

Now, table for $2x-y=0$ or
$y=2x$
Here, the lines intersecting at point C ($\frac{3}{2},3)$

The coordinates of the vertices of $△COB$ are C ($\frac{3}{2}$, 3), O(0, 0) and B(3, 0).

Area = A = $\frac{1}{2}\times base\times height=\frac{1}{2}\times 3\times 3=\frac{9}{2}=4.5$ sq.units