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What does it mean for a system of linear equations to have no solutions?
It means that there is no set of values for the variables such that all the linear equations are simultaneously true.
How do you check a solution to a system of equations?
Put the values that you find (as the solution) back into one (or more) of the original equations and evaluate them. If they remain true then the solution checks out. If one equation does not contain all the variables involved in the system, you may have to repeat with another of the original equations.
Do you have to use the same variables for all equations when creating a system of equations?
The idea is to work with the same variables, but it is possible that some of the variables are missing in some of the equations.
If an equation is an identity what is true about the solution?
It is true for all permissible values of any variables in the equation. More simply put, it is always true.
What is the meaning of solution of an equation?
The solution to an equation consists of the value (or values) of all the variables such that the equation is true when the variable(s) take those values.
