How to Solve Equations by Making Appropriate Substitutions

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Certain types of equations need to be solved by substitution. Solve equations by making the appropriate substitution with help from an experienced educator in this free video clip.

Part of the Video Series: Lessons in Math
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Video Transcript

Hi, my name is Marija. I'm a mathematician, and today I'm going to show you how to solve equations by making appropriate substitutions. So we're going to start with the system of equations Y equals 4X plus 2 and we're going to start with 2X plus Y equals 20. So when making substitutions if you already have an equation that's solved in terms of one variable and that's the equation you want to use to substitute. So because I already know what Y is in terms of X I want to take this piece and substitute it in for Y so I have Y equals 4X plus 2, that means that I'm going to take this 4X plus 2 and substitute it in for Y into my other equation. So I'm going to rewrite this first equation 2X plus Y equals 20 and now I'm going to substitute 2X plus, now instead of writing Y I'm opening parentheses and I'm going to replace it with its equivalent in terms of X, 4X plus 2 equals 20. Now I have an equation and one variable so now I can solve it. I'm going to go ahead and combine like terms, 2X plus 4X is equal to 6X plus 2 is 20. I'm going to use inverse operations to try to get X alone so I'm going to have 6X equals 18 after I have subtracted by 2 on both sides and then lastly I'm going to go ahead and divide by 6 on both sides and when I do that I'm going to get X equals 3 and then if you wanted to go ahead and solve the entire system, I would take the X and replace it back into my first equation, 4 times 3 is 12 plus 2 is 14, that means that Y is equal to 14. My name is Marija and I just showed you how to solve equations by making appropriate substitutions.


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