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Solving Systems of Equations using Elimination - Problem 1

Teacher/Instructor Alissa Fong
Alissa Fong

MA, Stanford University
Teaching in the San Francisco Bay Area

Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts

Solving a system of equations by elimination requires adding together two equations in a way that eliminates one of the variables so that you can solve for the other variable. Adding two additive inverses will eliminate those terms. Remember that when you add a number to its additive inverse, the result is 0. For example, x and -x are additive inverses. So is 2y and -2y. If two equations already have additive inverses -- meaning either the x or the y variables of the equations are additive inverses of each other -- then add the two equations together in order to eliminate that variable. Next, solve for the unknown. Remember that the solution of a system of equations is a coordinate point, so you need to find both the x and y value of that point. Check your answer by plugging the x and y value of the solution into both equations and simplifying. If the equations are true, then the solution is correct.

In this problem I'm given a system of equations which is two equations with two variables and I'm asked to solve it using elimination. Elimination is when I want one of the variables to be eliminated by adding together the two equations and having coefficients that are additive inverses, that way a variable will like cancel out or have a sum of 0.

Here's what I mean in this equation, it's totally set up for elimination because my coefficients of the Xs are additive inverses, +1 and -1. Check it out when I add y plus -5y I get that –x plus x is 0 Xs and then 5 take away 9 is -4. Now I have a really easy equation with just one variable that I can solve without too much difficulty.

Divide both sides by -4 so I can see y is equal to 1. You guys I'm half way done with the problem already and that took me like 30 seconds. So the next thing I need to do is find the x coordinate that goes with this y coordinate by using either original equation and substituting in what I got for y. I'll use the first one. 1 take away some number, x, is equal to 5. I solve for x I'll have -x is equal to 4 so x is equal to -4. Substitute that in here and I have what I think is the solution to my system of equations.

Before I move on though I'm going to check to make sure I didn't make any errors especially with all those minus signs. I want to make sure that my y value take away my x value is equal to 5. Good that's true for the first equation. Let's look at the second equation. -5 times my y value plus my x number should be equal to the -9. -5 plus -4 good it's equal to -9. I checked it in both original equations that's how I know that I did everything correctly and I have the right solution.

So you guys for many students elimination is the favorite method for solving systems especially when you have it set up where the coefficients are additive inverses. Look for this in your homework it's going to make your homework go so much more quickly if you can use elimination on these problems that are much easier to use elimination instead of like substitution or graphing or matrices.

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