Maths

__ 7x+11y Investiagation __

1. Multiples of 7: 7,14,1,28,35,42,49,56,63,70 Multiples of 11: 11,22,33,44,55,66,77,88,99,110

2. Values for X and Y (Positive)
 * POSITIVE INTEGERS ||
 * X || 8 ||
 * Y || 4 ||


 * POSITIVE INTEGERS ||
 * X || 8 ||
 * Y || 4 ||

3. Negative Integers for X and positive for Y


 * X || Y ||
 * -3 || 11 ||
 * -14 || 18 ||
 * -21 || 121 ||
 * -25 || 25 ||

Positive Integers for X and Negative integers for Y
 * X || Y ||
 * 52 || -24 ||
 * 41 || -17 ||
 * 30 || -10 ||
 * 14 || -3 ||
 * 9 || -3 ||

Equations that can work: When x is negative the equation can be: -11n+8 Examples that we can use to prove this is true: -11(4)+8 -44+8= -36

-11(5)+8 -55+8=-47

When y is negative the equation can be: -7n+4 Examples that we can use to prove this is true:

-7(5)+4 -35+4=-31

-7(4)+4 -28+4= -24

Explanation: For each step I did the same method but using different numbers. What I first did was to list the multiples of 11 and 7, until I found two integers that when added gave me 100. To find the negative integers in X, the first step I worked was to find numbers that when added with a multiple of 11, could give me the answer. In the beginning it was complicated because we had to use negative numbers, but when finding a certain amounts that could work, you could easily find many more. To find the negative integers in X became really easy when I found that if you choose a negative number and you add 100 the next digit you got was supposed to be positive, so when you came to try the equation it worked. To find the nth term I had to order the numbers, we could also find the nth term for Y as we did for X (Ordering the numbers). Each stage took me to a conclusion, until I found the equations.