Q. 205.0( 1 Vote )
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 y - axis:
5x – y – 7 = 0, x – y + 1 = 0.
Answer :
We can rewrite the equations as:
5x – y = 7
& x – y = - 1
For equation, 5x – y = 7
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, x – y = - 1
Plot the values in a graph and find the intersecting point for the solution.
Hence, the solution so obtained from the graph is (2,3), which is the intersecting point of the two lines.
The vertices of the formed triangle by these lines and the y - axis in the graph are A(2,3), B(0,1) and C(0, - 7).
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) = 1/2 × 8 × 2
[∵ Base = OB + OC = 1 + 7 = 8 units & height = 2 units from the y - axis to the point A]
Area(∆ABC) = 8 sq. units
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