Now it is in fact possible for an equation to have no solutions or infinite solutions.
An equation getting infinite solutions would mean that you could choose any number for the variable ( ex. x or y ), and that number would make the equation true. To represent an equation with infinite solutions we'd use the infinite symbol.
An equation getting no solutions would just that. It would mean the equation has no solutions what so ever. You could plug in any number for the variable and every single time you would get no solution. In addition to the equation having no solutions, this would also mean that the equation is not true can never be true. To represent an equation with no solutions, we'd use a symbol that is a zero with a diagonal line through it.
