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Solving Systems of Linear Equations using Elimination

Solving Systems of Linear Equations using Elimination 1.6 - Solution

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a
We want to solve the system using the elimination method. We then need to eliminate one of the variable terms when one equation is added to or subtracted from the other. For that to happen we first need to manipulate one or both equations. Let's multiply Equation (I) by as this will make the -terms get opposite coefficients.
This give us the following system of equations. If we add the equations the -terms will eliminate each other. We will find by solving the resulting equation. To find we can substitute for in any of the original equations. Let's use Equation (I).
We have found the solution to the system of equations and it is
b
Here we are going to use the elimination method to solve the following system of equations. To solve a system of linear equations using the elimination method, one of the variable terms must be eliminated when one equation is added to or subtracted from the other equation. Here it is necessary to first manipulate one or both equations. Let's multiply Equation (II) by as this will give the -terms opposite coefficients.
After manipulating Equation (II) we have the following system of equations. Let's go on and add these equations as this will lead to the -terms eliminating each other. By solving the resulting equation we will find Next we want to find We will do that by substituting for in any of the original equations. Let's use Equation (I).
We have now solved the system and its solution is