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 $$C(4, 0)$$.MathematicsRS AgarwalStandard X

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