How to Do Substitution in Math With Both Y Values

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Substitution is one of the methods used to solve a system of equations which is used to solve for where two lines actually meet. Find out how to do substitution in math with both Y values with help from an experienced mathematics professional in this free video clip.

Part of the Video Series: Math Calculations
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Hi, I'm Drew Moyer, and this is how to do substitution in math with both Y values. Substitution is one of the methods used to solve a system of equations which is used to solve for where two lines actually meet. So if I'm given two equations, I can use this method to find out the point at which they intersect. Let's say I have these two equations, Y equals 3X minus 5 and Y equals negative 1/2X plus 2. Now substitution involves the principle that if both of these things are equal to Y then they must also be equal to each other. So I will set them equal to each other like this, 1/2X plus 2 and now you can see I have only one variable which I can solve for. So I'm going to multiply everything by 2 to get rid of this fraction, 6X minus 10 equals negative X plus 4, then I will bring this X over to this side by adding it, 7X minus 10 equals 4 and then I will add 10 to both sides, 7X equals 14. Lastly I will divide both sides by 7, X equals 2. So now I have one half of the things I am looking for. I have an X coordinate. To get my Y coordinate, all I'll have to do is plug this value back into either of the two equations and solve for Y. So I will pick the first one, Y equals 3 times the quantity 2 minus 5, Y equals 6 minus 5, Y equals 1. So the answer to this system of equations is 2, 1 and that will be the point that both of these lines intersect. I'm Drew Moyer and this is how to do substitution in math with both Y values.

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