Q. 113.6( 8 Votes )
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.
Answer :
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.
Now similarly solve for equation, 2x + 3y = 4
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
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