math

Math investigation. 7x + 11y = 100

Lets work out the values for X and Y:

7 93 14 86 21 79 28 72 35 65 42 58 49 51 56 44 63 37 70 30

7 x 8 = 56 11 x 4 = 44 x= 8 y= 4

Now with negatives:

-7 107 -14 114 -21 121 -28 128 -35 135 -42 142 -49 149 -56 156 -63 163 -70 170 -77 177 -84 184 -91 191 -98 198 -105 205

7 x -3 =-21 11 x 11 = 121 x= -3 y= 11

7 x -14 = -98 11 x 18 = 198 x= -14 y= 18

I did the same procedure but with negatives for Y. the answers I got were: x= 19 y= -3 x= 30 y= -10

This are the total list i found for X and Y:

x= -14 y= 18 x= -3 y= 11 x= 8 y= 4 x= 19 y= -3 x= 30 y= -10

I noticed a pattern. The X values are increasing by 11. The Y values are decreasing by 7. I worked out a nth term formula for X and Y:

x= n+11 y= n-7

Example: 30 + 11 = 41 -10 - 7 = -17

41 x 7 = 287 -17 x 11 = -187 287 + -187 = 100

The nth term formula works.

the general rule for X is: X = 11n - 25

the general rule for Y is: Y = -7n + 25