Alana's Algebra Aide!


This page was created by a struggling Algebra student. It was designed for other struggling Algebra students. On this page you will learn how to Solve Linear Combinations, use the Substitution Method, and also how to Solve Word Problems. I hope you find all you need! Enjoy, and good luck!


How to Solve Linear Combinations:

3x + 2y =
12                                                In solving Linear Eqautions, you need to find the variable easiest to cancel out.
6x - 2y =  6                                                  In this paticular problem you would choose Y because it already has the same
9x = 18                                                        numbers and has opposite signs. Once the Y is gone then you have to combine
9x/9 = 18/9                                                  your X's. This would leave you with your X and with you answers which you
x = 2                                                            also have to combine. Once they are together you have you division. Divide your
3(2) + 2y = 12                                             X by your answer and then you have found your X. Your not done yet!! Now 
6 + 2y = 12                                                  you have to substitute your answer for X in the place of X in the first problem.
2y = 18                                                        Peice of cake!!!
2y/2 = 18/2
y = 9


How to Use the Substitution Method:

5x - 10y  = 20                                              In this type of problem, you use the given variable in place of the variable in the
y = 4 + 2x                                                    question. If you don't have one given, you can make one you self by rearranging  5x - 10(4 + 2x) = 20                                    the varaiables. In this question, replace the Y variable with what Y equals. After
5x - 40 - 20x = 20                                       this, combine like terms and keep only your varaiables on one side and then you
-15x = 60                                                    use your basic algebra skills and solve for X. Once you have this you can substi-
x = - 4                                                         tute for the Y in the first problem as well. These problems are easy! Don't worry!
5(- 4) - 10y = 20
-20 - 10y = 20
- 10y = - 40
y = 4


How to Solve Word Problems:



A delivery truck arrives at the Roberts’
store with 8 small boxes and 5 large boxes.
The total charge for the boxes, without tax
or delivery charges, is $184.  A large box
costs $3 more than a small box. What is
the cost of each size box??

8s + 5l = 184
l  = 5 + 3
8s + 5(5 + 3) = 184
8s + 25 + 15 = 184
8s = 104
s =  13
8(13) + 5l = 184
104 + 5l = 184
5l = 80
l = 13
84
In this problem you should look first at the numbers. Seperate them and give them variables. S and L would fit for small and large. Then you look for the other problem. Once you see what they are looking for you can easily set the problem up. Once it is set up it is a substitution problem. Those are easy so have fun!!!!

           

If you have any other questions on how to solve any problems,
another great website is Purplemath.com