Question

Question 7
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
$\Rightarrow$ x = y -1
$\begin{array}{cccc}x& 0& 1& 2\\ y& 1& 2& 3\end{array}$
3x + 2y - 12 = 0
$\Rightarrow$ $x=\frac{12-2y}{3}$
$\begin{array}{cccc}x& 4& 2& 0\\ y& 0& 3& 6\end{array}$
Graphical representation:

From the figure, it can be observed that these lines are intersecting each other at point (2, 3) and x-axis at ( - 1, 0) and (4, 0). Therefore, the vertices of the triangle are (2, 3), ( - 1, 0), and (4, 0).