Nichole's Nifty Equations   
 

My name is Nichole P. I am in Mrs. Felz Algebra ll class. This page is designed to help and teach people how to solve linear equations. I will have examples of substitution, elimination, and linear word problems.
Elimination Method:
Your equations are...
5x-2y=4
3x+y=9 

(2) 3x+y=9            5(2)-2y=4
6x+2y=18             10-2y=4
5x-2y=4               -10     -10
                           -2y=-6
11x = 22               -2    -2>
11      11                  y=3
x=2 

 

      You are solving this equation by using the elimination method. The first thing you want to do is eliminate the y so that you may get x by its self. You would now want to multiply the first problem by -2 so that you may 'kill' the y. So now you have 6x+2y=18. You then add the first equation to the new one and get 11x=22. Then divide to get your x which equals 2.
    Now, you substitute the x for 2 and solve. You then have 10-2y=4. You minus 10 from both sides and end up with -2y=-6. Now you can have your answer by simply dividing and come up with y=3. Now your answer is (2,3)
Substitution Method:
Your equations are...
y=5-4x      &     3x-2y=12

y=5-4(2)           3x-2(5-4x)=12
y=5-8                3x-10+8x=12
y=-3                      +10       +10
                             11x=22
                                11    11
                                    x=2

 You are solving this equation bye the Substitution method. The first thing you want to do is findx.. In this equation, y is already given to you, so all you need to do is substitute in the other equation. So you are going to fill in 3x-2(5-4x)=12. Then solve. You add 10 to both sides and end up with 11x=22. Now you must divide and end up with x=2. Now you are done and your answer is (2, -3) 
Word Problem:
    One day a store sold 45 pens, one kind at $3.95 and another kind at $9.75. In all, $398.75 was taken in. How many of each kind was sold?

Your equations are:
x+y=45 OR y=x+45
8.95x+ 9.75y= 398.75

 In this equation, you will be solving a word problem using substitution or elimintaion. From the word problem you will find 2 equations and choose which method you will use and work from there.

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