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  • Draw the graph of the pair of equations 2x + y = 4 and 2x – y = 4. Write the vertices of the triangle formed by these lines and the y-axis. Also find the area of this triangle.

Draw the graph of the pair of equations 2x + y = 4 and 2x – y = 4. Write the vertices of the triangle formed by these lines and the y-axis. Also, find the area of this triangle.

Answers (1)

Solution:
The given equation are:
2x + y = 4
2x –y = 4
2x + y = 4

x 0 1 2

 

y 4 2 0

2x-y=4

x 0 1 2
y -4 -2 0

Hence from the above graph, it is clear that both the lines and y-axis make triangle ABC.

Now, the area of triangle ABC is

2(area of \bigtriangleupAOB)

2\left ( \frac{1}{2}\times OB\times OA\right )

2\left ( \frac{1}{2}\times 2\times 4\right )
2(4)
8 sq. units.
Hence, the required area of a triangle is 8 sq. units.

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infoexpert27

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