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 \((4, 0).\)