when solving linear equations what does it means to have infinite solutions, what does it mean to have no solutions and what does it mean to have one solution

Answer 1

When solving a linear equation, the number of solutions can vary. Here is what each scenario means:

1. Infinite solutions: When a linear equation has infinite solutions, it means that every possible value for the variable in the equation satisfies the equation. This typically occurs when the equation is an identity, meaning both sides are equal for all values of the variable. In this case, the solution set is all real numbers.

2. No solutions: When a linear equation has no solutions, it means that there is no value for the variable that satisfies the equation. This typically occurs when the equation is a contradiction, meaning the two sides can never be equal. In this case, the solution set is the empty set.

3. One solution: When a linear equation has one solution, it means that there is only one value for the variable that satisfies the equation. This typically occurs when the equation is consistent and represents a line on a graph. In this case, the solution set is a single value for the variable.