![]() We can affirm that the points of the plane that satisfy this relation are solutions of the system (if we work with the second equation we arrive at the same result). This says that the two equations are equivalent, we solve one of the two equations. Now, let's verify that the previous system of equations has infinite number of solutions, note that if we multiply the first equation by 3, we get the second equation. When a system of equations has infinite solutions this does not guarantee that any point of the plane is a solution, we can verify this fact by taking the arbitrary point $(2 ,1)$ which does not satisfy any of the equations, for this reason it can not be a system solution.
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