= for the left side of the first equation, and it is identical to its right side Simply substitute the found values of, and into the original equations. Thus the solution of the original system of equations is,. Next, back-substitute the found values and into the first equation of the system (1): Now, substitute the found value of into the second equation of the system (4). In this way you cancel the terms with the unknown and immediately get the single equation To solve it, apply repeatedly the elimination method by distracting the first equation from the second one in the system (4). You got the system of two linear equations in two unknowns. The first step of the elimination method is completed. So, you obtained the system of two equations (2) and (3) in two unknowns and from the original system of three equations (1) Notice that the terms with are canceled in (3). Now multiply the first equation of the system (1) by and add it to the third equation: Multiply the first equation by and add it to the second equation: As the last step, back-substitute the two found values for unknowns into either appropriate of the original equations - it will allow you to find the last unknown.Įxamples below show how this method works.Įxample 1Solve the system of linear equations by the Elimination method Then back-substitute the found value into the intermediate system of two linear equations in two unknowns to get the second unknown. Again, you select the multipliers to cancel co-named variable terms for some unknown in the final equation.Īfter completing this, you will get the single linear equation in one unknown which you can easily solve. For it, you multiply both sides of the first equation of the obtained system to some number, multiply both sides of the second equation to another number and then to add both these equations. When it is done, you solve the obtained system of two linear equations by repeatedly applying the elimination method. After completing these steps, you reduce the original system of three linear equations in three unknowns to the system of two linear equations in two unknowns. Repeat this procedure for the first and the third equation. Then replace the second equation by this resulting equation. The multipliers are selected to cancel co-named variable terms for some unknown in the resulting equation. The Elimination method is to multiply both sides of the first equation to some number, to multiply both sides of the second equation to another number and then to add both these equations. In this lesson you will learn the Elimination method for solving systems of three linear equations in three unknowns. Solving systems of linear equations in 3 unknowns by the Elimination method
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