# Equivalent equations

The best way to handle equations in answers is the smart comparison mode of Equivalent equations. In this mode, two equations, inequations, or systems of, are equivalent if they have the same solutions ignoring multiplicity.

## Example 1: Equation of a line

Consider the following question:

with correct answer:

Then, the following answers will be accepted or rejected according to the table below:

Student answer | Validation |
---|---|

$\frac{y-2}{x-1}=3$ | |

$y-2=3x-3$ | |

$y=3x-1$ | |

$\frac{y}{3}+\frac{1}{3}=x$ |

## Example 2: Solve an equation

Note that the solutions are a particular case of equivalent equations. But you can not decide if an equation is solved yet, or is not. Beware, you should not use this mode to ask for solutions to equations. For example,

with correct answer:

Then, the following answers will be accepted or rejected according to the table below:

Student answer | Validation |
---|---|

$x=3$ | |

$3x=9$ | |

$2x-2=x+1$ |