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.

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Solution

Consider the given equation.x−y+1=0 ⇒y=x+1 3x+2y−12=0 ⇒y=6−3x2 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 ⇒x=−1 3x+0−12=0 ⇒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).

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