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.

Ans.For equation \( x – y + 1 = 0\), points which lie on the line:

\(\begin{array} {|r|r|}\hline x & 0 & 1 \\ \hline y & 1 & 0 \\ \hline \end{array}\)

For equation \( 3x + 2y – 12 = 0\), points which lie on the line:

\(\begin{array} {|r|r|}\hline x & 4 & 0 \\ \hline y & 0 & 6 \\ \hline \end{array}\)

Graph for the above equations is:



We can see from the graph that the point of intersection of the lines with each other is (2, 3) and the points of intersection with x - axis are :
(–1, 0) and (4, 0).

Thus, the coordinates of the vertices of the triangle formed are (2, 3), (-1, 0) and (4, 0).