Question

Draw the graphs of the equations $x-y+1=0$ and $3x+2y-12=0$. Determine the coordinates of the vertices of the triangle formed by these lines and the $x$-axis, and shade the triangular region.

Answer 1

$x-y+1=0$

$x-y=-1$ ...(i)

$3x+2y-12=0$

$3x+2y=12$ ...(ii)

$x-y=-1$

$y=1+x$

$x$	$0$	$-1$
$y$	$1$	$0$

Plot $(0,1)$ and $(1,2)$ on graph and join them to get eqn (i)

For $3x+2y=12$

$\Rightarrow 2y=12-3x$

$\Rightarrow r=\frac{12-3x}{2}$

$x$	$0$	$4$
$y$	$6$	$0$

Plot point $(0,6)$ and $(4,0)$ on graph and join them to get eqn (ii)

$△ABC$ is the required triangle with coordinates of $A$ as $(2,3),B(-1,0)$ and $C(4,0)$.