Maths+investigation

7x+11y=100

To find the values that can satisfy the equation I started by writing all the posible X positive values: 7,14,21,28,35 etc Then I wrote all the numbers that would add to these values that would give 100 as an aswer: 93,86,79,72,65 etc Then I looked for which of those numbers could be a possible Y value. And I only found one pair of numbers that would fit this criteria: 56 and 44 So the Equation would be 7(8) + 11(4) = 100.

Then I tried listing the possible negative X integers: -7,-14,-21,-28,-35 etc

and I found 3 more pairs of numbers that fitted the criteria: -21,121 7(-3) + 11(11) = 100 -98,198 7(-14) + 11(18) = 100 -175,275 7(-25) + 11(25) = 100

With these 4 examples I can already notice a pattern. The value representing X in each equation decreases by 11 and the value representing Y increases by 7 every time. Now this gives a negative number for X and a positive for Y. So if we we want to get positive number for X and a negative for Y we simply need to add 11 to X and subtract 7 to Y. E.G. 7(19) + 11(-3) = 100 133 + -33 = 100

So an equation that would give the N value of X or Y would be something like this: X= 8-(11n-11) Y= 4+(7n-7) The number given for N should be the same in both equation should be the same to get the pair. To get a positive answer for X you would need to give a negative number for N and vice versa. So the final equation would be: 7(8-(11n-11) + 11(4+(7n-7) = 100