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

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Solution

$x - y + 1 = 0$
$x - y = - 1$ ...(i)
$3 x + 2 y - 12 = 0$
$3 x + 2 y = 12$ ...(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 $3 x + 2 y = 12$
$\Rightarrow 2 y = 12 - 3 x$
$\Rightarrow r = \frac{12 - 3 x}{2}$

$x$ $0$ $4$
$y$ $6$ $0$
Plot point $(0, 6)$ and $(4, 0)$ on graph and join them to get eqn (ii)
$△ A B C$ is the required triangle with coordinates of $A$ as $(2, 3), B (- 1, 0)$ and $C (4, 0)$ .

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