1 | initial version |

In the first case, x is fixed ans y is the unknown. In the second case, y is fixed ans x is the unknown. In the third case, both x and y are unknown, and the set of solutions is of dimension 1, hence the need for a parameter r1.

The fact that the parameter r1 is in direct bijection with y is only a consequence of the fact that your equation is very simple (affine).

2 | No.2 Revision |

In the first case, x is fixed ~~ans ~~and y is the unknown. In the second case, y is fixed ~~ans ~~and x is the unknown. In the third case, both x and y are unknown, and the set of solutions is of dimension 1, hence the need for a parameter r1.

The fact that the parameter r1 is in direct bijection with y is only a consequence of the fact that your equation is very simple (affine).

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