hey! someone answered this question but i still don't get how they got it

[fringe orchid]

can someone explain?

[orchid tundra]

you need to find what number you root to get 6

which is 36

so 3x + 2y = 36

[fringe orchid]

ohhh ok so then how did this person get x = 4?

[orchid tundra]

well im not exactly sure actually idk if the question is asking for two exact values or any values that could work for that equation

well we know that y is bigger than x so at this point I’d probably just do trial and error

but there’s probably a better way so im not sure

[tawdry raven]

I actually didn’t find the two pairs but you could just find the point of intersection of the lines and sub values of x that are greater than the x value you find for the point of intersection

thats cold by me 36 / 2 is 18 not 36 💀

if you do x = -1.5x + 18, youd get x = 7.2 so if you subtitute any integer x thats greater than 7.2 into the equation y = -1.5x + 18, you should get a pair of x and y that should satisfy the equation in the question

[silk goblet]

This is what is known as a "Diophantine equation" (where you have more variables than equations and are looking for only integer / positive integer solutions)

This one is fairly basic and i'll show u a technique to solve this one

We have 36 = 3x+2y

The main idea is kind of a very systematic trial and error

First observe that 36 is dividible by 2 so 3x+2y is divisible by 2 so x is divisible by 2 (since 2y is always even) (Side note: you can use this same logic to deduce that y is divisible by 3)

Since x<y we can start checking from the smallest value of x (which is divisible by 2)

If x=2 then 36=6+2y so y=15
If x=4 then 36=12+2y so y=12
If x=6 then 36=18+2y so y=9

If x=8 then 36=24+2y so y=6 but this is impossible since now x>y

Hence the possible solutions are (2,15) (4,12) and (6,9)

If this comes up on a gcse paper then you definitely don't have to go into all this detail and since the question just wants 2 sets of values for (x,y) the best thing u can do is trial and error

[silk goblet]

(y>x so the blue line should be on the other side of the line y=x and since x and y are positive then the blue line should stay in the top right quadrant)

[tawdry raven]

OH YEAH

whoops mb