find out whether the following pair of linear equations are consistent, or inconsistent.
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(i) We have,
x + y = 5 ...(i)
⇒ y = 5 - x
Thus, we have following table
2x + 2y = 10 ...(ii)
Thus, we have following table
When we plot the the graph of the equations we find that both the lines are coincident.
Hence, pair of linear equations has infinitely many solutions
x - y = 8
⇒ y = x - 8
Thus we have following table
Thus, we have following table :
When we plot the graph of the equations. We find the both the lines never meet.
Hence, lines are parallel and equation has no solution.
find out whether the following pair of linear equations are consistent, or inconsistent. 5x-3y=11 ; -10x + 6y = -22
Hence, the given lines are consistent. So, the given pair of linear equations has infinitely many solutions and therefore it is consistent.
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