MathematicsDetermine graphically whether the following pair of linear equations have which kind of solution. 2x−3y=8 4x−6y=16  

Determine graphically whether the following pair of linear equations have which kind of solution.


2x3y=8 4x6y=16  


  1. A
    unique solution
  2. B
    infinitely many solution
  3. C
    no solution
  4. D
    none of the above 

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    Solution:

    Given pair of linear equations are:
    2x3y=8 4x6y=16  
    We need to determine graphically what kind of solutions will the given pair of equations have.
    We have,
    2x3y=8 3y=2x8 y= 2x8 3 ...(i)  
    Now constructing value table based on equation (i), we have,
    Similarly, we have,
    4x6y=16 6y=4x16 y= 4x16 6 y= 2x8 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, it is clear that the lines overlap each other and hence, they have infinitely many solutions.
    Thus, the given pair of equations have infinite many solutions.
    Therefore, option 2 is correct.
     
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