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

$x − y + 1 = 0$ or $x = y − 1$

$x$	$0$	$1$	$2$
$y$	$1$	$2$	$3$

$3x + 2y − 12 = 0$
$x= 12-\dfrac{2y}{3}$

x	$4$	$2$	$0$
y	$0$	$3$	$6$

Hence, the graphic representation is as follows.

From the figure, it can be observed that these lines intersect each other at points (2, 3) and the $X$-axis at $(−1, 0)$ and $(4, 0).$

Therefore, the vertices of the triangle are $(2, 3), (−1, 0)$, and $(4, 0).$