IGCSE+Paper+6+Investigation


 * Andrea Aviles**

**IGCSE Paper 6 Investigation** First of all I gathered all the multiples of 7 such as (7, 14, 21, 28,...) and all the multiples of 11 such as (11, 22, 33, 44,...) I tried to find a pair of numbers that were positive and that would make 100 and I could only find one that satisfied the equation (Pair 1: highlighted in red)

__**56 + 44 = 100**__ 7x +11y = 100 X = 8Y=4 (8x7=56) (4x11=44)
 * (First positive equation)**
 * The values for X and Y in this equation are x=8 and y=4**

Now I will try to find negative integers for x with positive integers for y and vice versa. First I will make a chart that will include all the negative numbers and I will find more numbers that satisfy the equation of 7x+11y=100.

Key: the colors added to the graph show the mach in the equations

After I made this graph I realized that I couldnt find any equations with both negative numbers so I tried vice versa and this are the results I got

__-98 + 198 = 100__ 7x +11y = 100 X= -14 Y=18 (-14x7=-98)(18x11=198)

__-21 +121 = 100__ 7x +11 y = 100 X= -21 Y=121 X=-3 Y=11 (-3x7=-21) (11x11=121)

__364 +-264 = 100__ 7x +11 y = 100 X= 364 Y= -264 X= 52 Y= -24 (52x7=364) (-24x11=-264)

__-187 + 287 = 100__ 7x +11 y = 100 X=-187 Y=287 X=-27 Y=26 (-27x7=-187) (26x11=287)

__-375 +275 = 100__ 7x +11y = 100 X=-375 Y=275 X=-54 Y=25 (-54x7=-375) (25x11=275)

Now I will record my results in a table like this:

Afterwords I found a pattern that satisfies the equation and gets me to the next value X + -77 and Y + 77