How can I simulate data from an interval which needs to satisfy a constrain/condition?

I need to simulate uniformly data (two values: x and y) from an interval of possible numbers that obey a constrain/condition specified as A.x+B.y=M , where A,B and M are different given numbers. Specifically, suppose I have the following 3 constrains in the aforementioned notation: 2x+y=100 3x+2y=60 x+3y=80

Let's say that I need to generate 25 simulated data (i.e. 25 pairs of x and y) from EACH of these constrains. So, I would get 25 pairs, each of which will need to satisfy the respective constrain: 25 pairs for 2x+y=100; 25 pairs for 3x+2y=60, and 25 pairs for x+3y=80 Many thanks in advance

Answer 1

[Matt Tearle]

Do you need to generalize this? Because for this case you could just do:

x = 20*rand(75,1);
y = x;
y(1:25) = 100 - 2*x(1:25);
y(26:50) = (60 - 3*x(26:50))/2;
y(51:75) = (80 - x(51:75))/3;

You could reshape into matrices or other arrangements if you want the three sets separately. E.g.

X = reshape(x,25,3);
Y = reshape(y,25,3);

[Paulo]

Many many thanks for the precious help Matt! From what I can tell it should work. I'm now trying to use it with my data and if I encounter any other issues I will shout for help :-) All the best