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The answer depends on what are meant to be real numbers! If all the coefficients are real and the matrix of coefficients is non-singular, then the value of each variable is real.
No. For example, linear algebra, for example, is about linear equations where the domain and range are matrices, not simple numbers. These matrices may themselves contain numbers that are real or complex so that not only is the range not the real numbers, but it is not based on real numbers either.
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You would solve them in exactly the same way as you would solve linear equations with real coefficients. Whether you use substitution or elimination for pairs of equations, or matrix algebra for systems of equations depends on your requirements. But the methods remain the same.
The additive inverse is used to solve equations; equations, in turn, are used to model many real-world situations.