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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.


Solution

$$x-y+1=0$$
$$x-y=-1$$    ...(i)
$$3x+2y-12=0$$
$$3x+2y=12$$   ...(ii)
$$x-y=-1$$
$$y=1+x$$

$$x$$$$0$$$$-1$$
$$y$$$$1$$$$0$$
Plot $$(0, 1)$$ and $$(1, 2)$$ on graph and join them to get eqn (i)
For $$3x+2y=12$$
$$\Rightarrow 2y=12-3x$$
$$\Rightarrow r=\dfrac{12-3x}{2}$$

 $$x$$$$ 0$$$$ 4$$
 $$y$$$$ 6$$$$ 0$$
Plot point $$(0, 6)$$ and $$(4, 0)$$ on graph and join them to get eqn (ii)
$$\triangle ABC$$ is the required triangle with coordinates of $$A$$ as $$(2, 3), B(-1, 0)$$ and $$C(4, 0)$$.

497897_465369_ans.png

Mathematics
RS Agarwal
Standard X

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