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__Investigation__

The values of X and Y are the following:


 * **X** || **Y** ||
 * 8 || 4 ||
 * -3 || 11 ||
 * -14 || 18 ||
 * -25 || 25 ||

From this we notice that the difference between two consecutive //x// values is -11, and the difference between two consecutive //y// values is 7. So, the difference in 11//y// is 77, and the difference in 7//x// is -77. Using this we can work out the terms //x//n and //y//n.

This is the equation I came up with: //11(y//n //+7) - 7(x//n //-11) = 100//

If we substitute n with any of the //x// or //y// values, we can find more solutions to the equation 7//x +// 11//y = 100//

For example: //11(y//n //+7) - 7(x//n //-11) = 100//

//11(4 +7) - 7(8 - 11) = 100//

//11(11) - 7(3) = 100//

//121 - 21 = 100//

Here is another method:

//7x+11y=100// //7x8=56// //11+4=44// //56+44=100//

So the first value of //x// and //y// is: //(7x8)+(11x4)=100//

Another equation I found is: //(7x19)+(-3x11)=100//

//(133)+(-33)=100//

To find the next //x// and //y// values you may use this method:

//x//n - 11 = The next value of //x// //y//n + 7 = The next value of//y//

Using this method we can assume that the next values of //x// and //y// that are not in the table above are:

//x=-36// //y=32//

How do I know this?

Because the last values of //x// and //y// that I found are -25 and 25. So, if I subtract 11 from -25 and add 7 to 25, I get the next //x// and //y// values.

-25-11=-36 25+7=32