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, x - 2y = 2 and 3x - 6y = 0 , what kind of solution do they have?
Solution
The given set of linear equations is:
- x - 2y = 2
- 3x - 6y = 0
First, let's simplify the second equation by dividing it by 3:
x - 2y = 0
Now, we have two equations:
- x - 2y = 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.
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