Ten Standard >> Graph of pair of linear equations in two variables | Part -3

Example 2: Draw the graph with the equations 4x-3y-6=0 and x+3y=9. Determine the coordinates of the vertices of the triangle formed by these two lines and the y-axis. Find the area of the triangle.

Solution: 
   4x-3y-6=0
\(\Rightarrow\) 3y=4x-6
\(\Rightarrow\) y=\(\frac{4x-6}{3}\)...(1)

   x+3y=9
\(\Rightarrow\) \(3y=9-x\)
\(\Rightarrow\) y=\(\frac{9-x}{3}\)...(2)

 
from equation (1),  

So from equation (1) we get points (0, -2), (3, 2) and  (6, 6)

from equationon (2),  

So from equation (1) we get points (9, 0), (6, 1) and  (0, 3)

Area of \(\triangle\)APB=\(\frac{1}{2} \times base \times altitute\)
                  =\(\frac{1}{2} \times AB \times PM\)
                  =\(\frac{1}{2} \times 5 \times 3\)
                  =\(\frac{15}{3}\) squire unit
                  =7.5 squire unit