When the coefficients of one variable are opposites you add the equations to eliminate a variable and when the coefficients of one variable are equal you subtract the equations to eliminate a variable. In the elimination method you either add or subtract the equations to get an equation in one variable. However, the solution to a certain class of system of simultaneous equations does always converge using the Gauss-Seidel method. The goal is to get a variable to cancel when you add the. You can add the same value to each side of an equation. It just means that you have to go back and fix the system so that one of the variables will cancel. By doing this we transformed our original system into an equivalent system: x + 3y 7 5y 10. But sometimes Substitution can give a quicker result. We multiply the first equation by 3, and add it to the second equation. Once you get used to the Elimination Method it becomes easier than Substitution, because you just follow the steps and the answers appear. Another way of solving a linear system is to use the elimination method. The elimination method for solving systems of linear equations uses the addition property of equality. Solve the following system by the elimination method.
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