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Q: Can you solve an equation if it has no solution?

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You could call it "the answer" or "the solution".

There cannot be a solution without an equation to solve!

No, you can only simplify an expression. To solve for a variable, it must be in an equation.

its mean solve the problem, to fine the solution like what makes it work.

you will need 2 equations to solve an equation with 2 unknowns

When an equation is based on false assumptions, you know that it has not solution. At other times, you may be able to tell through trying to solve the equation and constantly failing.

An "extraneous solution" is not a characteristic of an equation, but has to do with the methods used to solve it. Typically, if you square both sides of the equation, and solve the resulting equation, you might get additional solutions that are not part of the original equation. Just do this, and check each of the solutions, whether it satisfies the original equation. If one of them doesn't, it is an "extraneous" solution introduced by the squaring.

You solve the equation the same way as you would any other equation. Whether the variable is a fraction or otherwise will only become clear once you solve the equation. In other words, you don't initially KNOW whether the solution will be a fraction or not.

The equation does not have a solution.

You cannot. x - 54 is an expression not an equation. An expression has no solution set since there is nothing to solve.

Solution. A solution of an equation is a number that satisfy the equation. This means that if you replace this number on the equation and check it, the equation will be true. When you solve an equation you can find some roots, but not all of them satisfy the equation. Thus always check your answers after resolving your equation, and eliminate as solution the answers that don't make the equation true or undefined.

plug the x coordinate in the x part of the equation and plug the y coordinate in the y's part of the equation and solve

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