Draw the graph of the equation 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.

Solution :

Given Pair of linear equations are :

x – y + 1 = 0 ……(i)

and 3x + 2y – 12 = 0 …….(ii)

first we find points for equation (i),

x	0	4
y = x + 1	1	5
Points	A	B

second we find points for equation (ii),

x	0	4
y = \(12 – 3x\over 2\)	6	0
Points	C	E

Now, plot the points A(0,1), B(4, 5) and join them to get AB.

Similarly, plot the points in second table i.e. points C, E and join them to form a line CE.

Clearly, the two lines AB and CE intersect each other at the point D(2, 3).

Hence, the solution of the given pair of linear equations is x = 2 and y = 3.

Hence, the triangle formed is having vertices with the coordinates : D(2, 3), E(4, 0), F(-1, 0).