Solve each of the following given systems of equations graphically and find the vertices and area of the triangle formed by these lines and the x - axis:

x – y + 3 = 0, 2x + 3y - 4 = 0.

We can rewrite the equations as:


x – y = - 3


& 2x + 3y = 4


For equation, x – y = - 3


First, take x = 0 and find the value of y.


Then, take y = 0 and find the value of x.


x



0



- 3



y



3



0



Now similarly solve for equation, 2x + 3y = 4


x



0



2



y



4/3



0



Plot the values in a graph and find the intersecting point for the solution.



Hence, the solution so obtained from the graph is ( - 1,2), which is the intersecting point of the two lines.


The vertices of the formed triangle ABC by these lines and the x - axis in the graph are A( - 1,2), B( - 3,0) and C(2,0).


Clearly, from the graph we can identify base and height of the triangle.


Now, we know


Area of Triangle = 1/2 × base × height


Thus, Area(∆ABC) =


[ Base = BO + OC = 3 + 2 = 5 units & height = 2 units]


Area(∆ABC) = 5 sq. units


11