MathematicsSolve the following pair of equations graphically: 2x+3y+4=0 2x−3y−8=0  Also, find the area of the region formed by the lines with the x -axis.

Solve the following pair of equations graphically:


2x+3y+4=0 2x3y8=0  


Also, find the area of the region formed by the lines with the x -axis.


  1. A
    x = 6, y = 0 and Area = 2unit s 2  
  2. B
    x = 0, y = 6 and Area = 4unit s 2  
  3. C
    x = 1, y = -2 and Area = 6unit s 2  
  4. D
    x = -2, y = 1 and Area = 8unit s 2   

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    Solution:

    We have been given two equations: 2x+3y+4=0   and 2x3y8=0  . We need to draw the graphs of these equations and further calculate the area bounded by these lines and x-axis.
    We have,
    2x+3y+4=0 3y=42x y= 42x 3 ...(i)  
    Now constructing value table based on equation (i), we have,
    Similarly, we have,
    2x3y8=0 3y=82x y= 82x 3 y= 82x 3 ...(ii)  
    Now constructing value table based on equation (ii), we have,
    Now, based on these two tables, the graph constructed is:
    From the graph we can observe that both of the lines intersect at (1,2)  , therefore the values of x and y will be 1 and -2.
    The area bounded by these lines and x-axis is in a shape of triangle.
    Area of triangle is given as: Area ABC=12(base)(height).
    From graph, we have,
    Base = 6 units
    Height = 2 units
    Since, the measurements cannot be negative, we have taken base as positive.
    Therefore, the area is given by:
    Area = 1 2 (6)(2)  
     Area = 12 2  
     Area = 6unit s 2  .
    Hence, the area of region bounded by the lines and x-axis is 6unit s 2  .
    Therefore, option 3 is correct.
     
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