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## Echelon Method

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**Echelon Method**Problem 2.1 # 23 Prepared by E. Gretchen Gascon**Step 2: Eliminate the x term**Use equation 1 and 2 Use the multiplication rule to get the coefficients of the x term opposites Next Add the two equations to get a new equation. Remember this equation it will be used later**Step 2: Eliminate the x term (cont.)**Use equation 2 and 3 Use the multiplication rule to get the coefficients of the x term opposites Next Add the two equations to get a new equation. Remember this equation it will be used later**Step 3: Use the two equations to eliminate the y term**Use the multiplication rule to get the coefficients of the y term opposites Next Add the two equations to get a new equation. You are now ready to create this new set of equations**The new system of equations**One equations has 3 variables, one has 2 variables, and one equation has only 1 variable.**Step 6**Solve the last equation (the equation with only one variable)**Step 7: Back Substitution**Start with the last equation (the simplest one)**There is more than one way to solve this problem**The next slides will assume that you worked with r1 and r2, then when to use r1 and r3. The work looks a bit different, however the end results are the same.**(alternative solution) Step 2: Eliminate the x term (cont.)**As demonstrated previous in step 2(slide #4) , you can use equation 2 and 3, however, you could have used equations 1 and 3 as well. This example uses 1 and 3 Multiply the r3 by -1 to get the coefficients as opposites Next Add the two equations to get a new equation. Notice that this equation can be solved for y already without further adding of equations .**Comments**• Was there anything about this PowerPoint presentation that you would like further explained? • Post comments or questions to the Main Forum.