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 xaxis, and shade the triangular region.

Explanation

Pair of linear equations are
implies x - y + 1 = 0 …..(1)
y = x + 1
`{:(x,0,1,-1,2),(y,1,2,0,3):}`
`therefore` Points on this line are (0, 1), (1, 2), (-1, 0) and (2, 3). Plot these points on the graph paper and join them to form a straight line.
and 3x + 2y - 12 = 0 ....(2)
implies `y = (12 - 3x)/(2)`
`{:(x,0,4,2,1),(y,6,0,3,4.5):}`
`therefore` Points on this line are (0, 6), (4, 0), (2, 3) and (1, 4.5). Plot these points on the same graph paper and join them to form another line which cuts the previous line at any point From the graph, we see that the two lines intersect each other at D(2, 3). So, DCF is the required triangle whose vertices are D(2, 3), C(-1, 0) and F(4, 0).

Also, area `(DeltaDCF) = (1)/(2) xx` base `xx` altitude
`= (1)/(2) xx (4 + 1) xx 3` square units
= 7.5 square units