How to Solve Equations by Substitution

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Solving equations by substitution requires substituting a known variable value from one equation for the unknown variable of a different equation. Change an equation with substitution in order to work with a single variable using help from a math teacher in this free video math lesson.

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Video Transcript

So how do you solve equations by substitution? Hi I'm Jimmy Chang and I have been teaching college math for nine years now and substitution is one of the most popular methods to solving systems of equations in Algebra courses and once you see how this works it is actually a nice method to solve and pretty straightforward and easy to get used to. So here is an example that we have for you today. Suppose you have two equations the first one being y = 3x plus 1 and 2x plus 4y = 18. Now the whole idea of substitution is. If you know what one variable in this case being y is equal to something else since you know that y is equal to 3x plus1 then what you can do is you can take this and use it for the second equation. Most of the time you only want to work with one variable as opposed to two so because of this fact that y is equal to 3x 1, you can take the 3x plus 1 and put it in in place of the y. So in another words your equation is now going to look like 2x plus 4 X 3x plus 1 = 18. It is a direct substitution. It actually makes the equation easier because you now go from having two unknowns to just one variable that you are solving for. After that you go ahead and just use the Algebra and go from there. So you have 2x plus 4 x 3x is 12x and 4 X positive 1 is a 4 and that is going to give you 18. The Algebra continues, combine your like terms, 2x plus 12x is 14x plus 4 and it is going to give you 18, subtract 4 on both sides and then you have 14x = 14 and then 14 X what number is going to give you 14. Well you divide and as a result you will have x = 1. So that is one answer. However, remember because you have x and y you need to find out what the y is. But the good news is you know what x is, x is 1. So what you want to do is you want to plug the 1 back into any one of the red equations that I have up here. Now because y is already by itself in this case it is easier to plug in 1 in place of x over here. So here is what we have. Y = 3 X 1 plus 1, you know 3 X 1 is going to give you 3 and then at the 1 you can have a grand total of y = 4.

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