Question

Solve the following system of linear equations graphically:
$3x+y-11=0,x-y-1=0.$
Shade the region bounded by these lines and $y$-axis. Also, find the area of the region bounded by the these lines and $y$-axis.

Answer 1

Given,

$3x+y-11=0$

$\Rightarrow 3x+y=11$........(1)

$x-y-1=0$

$\Rightarrow y=x-1$......(2)

substitute the value of "y" in (1), we get,

$3x+(x-1)=11$

$\therefore x=3$

$\therefore y=2$

$(x,y)=(3,2)$

area of triangle formed by vertices $a(3,2),b(0,11),c(0,-1)$

$A=\frac{1}{2}\times BC\times AD$

$=\frac{1}{2}\times 12\times 3$

$=18sq.units$