| Hello, my name is Amber and I am a junior at Union Grove High School. I am in Mrs. Felz's sixth period Algrebra II class. This web page is to help explain how to use the substitution and elimination methods for solving linear equations. Also I will show you how to solve word problems. |  |
| Substitution Method:
Your equations are: y = -x+6 x-2y = -6 x-2y = -6
y = -x+6
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In these equatioins you are triyng to find the value for the "x" and the "y" and the method you are using is substitution. In order to use this method you have to put one of the equations in y=mx+b form, you already have y = -x+6 in y=mx+b form. You will then plug the (-x+6) in the place of the "y" in the second equation x-2y = -6. Now slove for the "x". Once you get the "x" value, plug the answer for "x" into the other equation, ( -x+6). Now solve for the "y". Once you get these two answers put them in an ordered pair, (x,y). You have now used the substituion method. |
| Elimination Method:
Your equations are: 5x-2y = 4 3x+y = 9 5x-2y = 4
3x+y = 9
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In these equations you are trying to find
the value for the "x" and the "y" and the method you are going to use is
elimination. In this method you are trying to eliminate or get rid
of either your "x" or your "y" in order to solve an equation. In
the given equations it would be easier to multiply the bottom equation
by 2 so that the equations now look like: 5x-2y = 4
now the " 2 y's" cancel
6x+2y = 18 each other out and you can solve for the "x". When you get the "x" value plug it into one of the two equations and solve for the "y". Once you get these two answers put them in an ordered pair, (x,y). You have now used the elimination method. |
| Word Problems:
One day a store sold 45 pens, one kind at $8.95 and another kind at $9.75. In all, $398.75 was taken in. How many of each kind was sold? Your two equations are:
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In these equations you are trying to solve a word problem, but in order to do that you must come up with two equations that are in the word problem. Once you come up with the two equations you are to solve the equations by either using the elimination method or the substitution method. Then, depending on which of the methods you choose, follow the above instructions on how to solve the equation. |