Math

7x+11y=100 Investigation

Multiples of 7: 7,14,21,28,35,42,49,56,63,70 Multiples of 11: 11,22,33,44,55,66,77,88,99,110 Possible values for X and Y: (Positive Integers)
 * X ||  Y  ||
 * 8 ||  4  ||

Possible Values for X and Y: (Negative Integers)
 * X ||  Y  ||
 * -3 ||  11  ||
 * -14 ||  18  ||
 * 30 ||  -10  ||
 * 19 ||  -3  ||

Values found for X and Y: (Negative and Positive Integers) Equation: When X is negative the equation is: -11n+8 Example: -3, -14 -11 times 1 = -11 + 8 = -3 -11 times 2 = -22 + 8 = -14
 * X ||  Y  ||
 * -14 ||  18  ||
 * 30 ||  -10  ||
 * -3 ||  11  ||
 * 8 ||  4  ||
 * 19 ||  -3  ||

When Y is negative the equation is: -7n+4 Example: -3, -10 -7 times 1 = -7 + 4 = -3 -7 times 2 = -14 + 4 = -10

The explanation of how I got the pattern: I got this pattern but first I found integers that are represented by X and other by Y. The ones that are X I multiplied them by 7 and the ones that are Y are multiplied by 11. When I tried to find the pattern I plot the numbers of X in order so I could find the nth term, when X is negative and Y is positive that is the nth term for that. The nth term for Y when its negative I found it by doing the same as when I found X is negative and Y is positive but now the other way.

Explanation of each stage: In the first stage I try to find out two integers that are positive but one is multiplied by 7 and other by 11. In the second step I tried to find out negative integers but 1 of both one of Y and one of X, I find out 4 so I can found then the pattern and explain each equation. Then I explain each pattern with all the equations, for, when X is positive Y is negative and when X is negative Y is positive try to explain how I got them by the results I could get.

END OF INVESTIGATION