Question

Draw the graphs of $$x-y+1=0$$ and $$3x+2y-12=0$$. Determine the coordinates of the vertices of the triangle formed by these lines and $$x$$-axis and shade the triangular area.

Solution

Given,$$x-y+1=0$$....(1)$$3x+2y-12=0$$....(2)put $$x=0$$ in (1)$$0-y+1=0\Rightarrow y=1$$$$(0,1)$$.....(a)put $$y=0$$ in (2)$$3x+2(0)-12=0\rightarrow x=4$$$$(4,0)$$.....(b)put $$x=0$$ in (2)$$3(0)+2y-12=0\rightarrow y=6$$$$(0,6)$$......(c)put $$y=0$$ in (1)$$x-0+1=0\Rightarrow x=-1$$$$(-1,0)$$...(d)From figure, the vertices of triangle are $$(-1,0),(2,3),(4,0)$$Mathematics

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