Elimination is particularly easy when one of the coefficients is one, or the equation can be divided by a number to reduce a coefficient to one. This makes substitution and elimination more trivial.
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Gaussian elimination is used to solve systems of linear equations.
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.
Elimination and substitution are two methods.
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You cannot solve one linear equation in two variables. You need two equations that are independent.