Question

Draw the graphs of the following linear equations on the same graph paper:

$2x+3y=12,x-y=1$

Find the coordinates of the vertices of the triangle formed by the two straight lines and the y-axis. Also, find the area of the triangle.

Answer 1

$2x+3y=122x=12-3yx=\frac{12-3y}{2}Ify=0,thenx=\frac{12-3\times 0}{2}=\frac{12-0}{2}=\frac{12}{2}=6Ify=4,thenx=\frac{12-3\times 4}{2}=\frac{12-12}{2}=\frac{0}{2}=0\begin{array}{ccc}x& 6& 0\\ y& 0& 4\end{array}$

Now plot the points (6, 0 ) (0, 4) on the graph to get a line.

$x-y=1\Rightarrow x=1+yIfy=0,thenx=1+0=1Ify=1,thenx=1+1=2\begin{array}{ccc}x& 1& 2\\ y& 0& 1\end{array}$

Now plot the points (1, 0) and (2, 1) on the graph to get another line.

Co-ordinates of E, F, B are E (3, 2), (0, -1) and (0, 4).

Area of the triangle FEB so formed = $\frac{1}{2}\times FB\times EL$

$=\frac{1}{2}\times 5\times 3=\frac{15}{2}=7.5sq.units$