Question

Solve graphically the pair of linear equations: $4x-3y+4=0,4x+3y-20=0$. Find the area of the region bounded by these lines and $x$-axis

• A. $12$ sq. units
• B. $18$ sq. units
• C. $9$ sq. units
• D. $13$ sq. units

Answer 1

The correct option is A $12$ sq. units

$4x-3y+4=0$

$⟹x=\frac{-4+3y}{4}$

Let, $y=4$, then $x=\frac{-4+3\left(4\right)}{4}=2$

Similarly, when $y=0,x=-1$

$4x+3y-20=0$

$⟹x=\frac{20-3y}{4}$

Let, $y=4$, then $x=\frac{20-3\left(4\right)}{4}=2$

Similarly, when $y=0,x=5$

Plotting the above points on the graph, we get, the intersecting point i.e$(2,4)$

Area of the region bounded by these lines and x-axis $=\frac{1}{2}\times 6\text{units}\times 4\text{units}$

$=12\text{sq. units.}$