Question

Solve graphically the following system of equations $x-y+1=0$ and $3x+2y-12=0$. Determine the co-ordinates of the vertices of the triangle formed by these lines and the x-axis and shade the triangular region.

Answer 1

Consider the given equation.

$x-y+1=0$

$\Rightarrow y=x+1$

$3x+2y-12=0$

$\Rightarrow y=6-\frac{3x}{2}$

Consider the graph shown below.

Point $(2,3)$ is the point of intersection. So, it is the solution of both the equations.

Now, at x-axis, $y=0$. So,

$x-0+1=0$

$\Rightarrow x=-1$

$3x+0-12=0$

$\Rightarrow x=4$

Therefore, coordinates of the vertices of the triangle formed by both the lines and the x-axis are $(2,3),(-1,0)$ and $(4,0)$.