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Finding Solutions of Systems of Linear Equations

Compare the advantages and disadvantages of substitution and elimination methods with the matrix method to solve systems of linear equations and the relationship these have with matrix method solving.

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The substitution method works very well when one of the equations in the system is already solved for one of the variables or can be easily solved for one of the variables. Once that equation is solved for one of the variables, the resulting expression can be easily substituted into the other equation(s) to remove that variable from the system. A simple example looks like this:

y = x + 6
x + y = 4

Notice that the first equation is already solved for y. This means that you can take the equivalent expression (x + 6) and substitute it in place of y in the second equation to get x + (x + 6) = 4. You can then solve this equation to get a value of x of -1. Then since y = x + 6, substituting -1 in for x gives a y value of 5 and the solution of the system is (-1,5).

Even though any linear equation can be solved for one ...

Solution Summary

Systems of equations can be solved in one of many different methods. A comparison is given among the substitution, elimination, and matrix methods for solving systems of linear equations.