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Mat/116

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Submitted By Bigshaka
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Week 6 DQ 2

· What are two techniques used to solve systems of linear equations? Which do you feel is better? Explain why. Write a system and show us how you would use your favorite solution method.
The two symbolic techniques used to solve linear equations are substitution and elimination methods. The substitution method consist of solving for one of the variables in one of the equations, then substituting the value/solution of that variable into the other equation, which when solved will give the values of both variables. The elimination method consists of using the addition property of equality, which by adding or subtracting the equations one of the variables can be eliminated and solved for the variable that is left. Then, the value of that variable can be substituted into one of the original equations to solve for the second variable, which when solved will give the solutions to the equations.I think both methods are beneficial; however, I sometimes prefer the elimination method because it allows one to eliminate one of the variables and obtain the value of the other variable, then one can use that to find the value of the eliminated variable.However, I think whichever method is used it is important to read the problem correctly and to check ones work.
For example: x + y = 6
-x + 3y = 6
Eliminate x-variable: x + y = 6
-x + 3y = 6
4y = 12 y = 3
Substitute: x + 3 = 6 x = 3
Ordered Pair: (3,3)
Check Work: x + y = 6 -x + 3y = 6
3 + 3 = 6 -3 +3(3) = 6
6 = 6 -3 + 9 = 6
6 = 6

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