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For the given set of linear equations, x - 2y = 2 and 3x - 6y = 0 , what kind of solution do they have?

Question

For the given set of linear equations,

x2y=2 x - 2y = 2
3x6y=0 3x - 6y = 0

what kind of solution do they have?

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Solution

The given set of linear equations is:

  1. x - 2y = 2
  2. 3x - 6y = 0

First, let's simplify the second equation by dividing it by 3:

x - 2y = 0

Now, we have two equations:

  1. x - 2y = 2
  2. x - 2y = 0

These two equations are parallel lines because they have the same coefficients for x and y. However, they have different constant terms on the right side of the equation (2 and 0).

Therefore, these two equations have no solution because parallel lines never intersect.

This problem has been solved

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