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.

Answer 1

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)

$3x+2\left(0\right)-12=0\to x=4$

$(4,0)$.....(b)

put $x=0$ in (2)

$3\left(0\right)+2y-12=0\to y=6$

$(0,6)$......(c)

put $y=0$ in (1)

$x-0+1=0\Rightarrow x=-1$

$(-1,0)$...(d)

From figure, the vertices of triangle are $(-1,0),(2,3),(4,0)$