Find all possible ordered pairs that satisfy a linear equation

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Kathleen Horvath 2021-5-16

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回答： Star Strider 2021-5-16

I am trying to find all possible combinations of X and Y that satisfy the following linear equation:

f = ((X*25)+(Y*(24))) == 100

The variables should only be evaluated in the following range:

1 ≤ X ≥ 7 and 0.1 ≤ Y ≥ 3 or put another way X = 1:0.01:7 and Y = 0.1:0.01:3

I assume there are multiple simple ways to solve this using either for loops or syms approaches.

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Answer 1

Star Strider 2021-5-16

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The ‘all possible’ criterion would produce infinite solutions. I suspect you would spend the rest of your life calculationg it!

Here is a slightly more limited calculation —

B = 1;
k = 1;
while (B>=0.1) & (B<=7)
    X(k,:) = k/10;
    B = (100 - X(k,:)*25)/24;
    Y(k,:) = B;
    k = k+1;
end
Result = table(X,Y)
Result = 40×2 table
XY_________

    0.1    4.0625
    0.2    3.9583
    0.3    3.8542
    0.4      3.75
    0.5    3.6458
    0.6    3.5417
    0.7    3.4375
    0.8    3.3333
    0.9    3.2292
      1     3.125
    1.1    3.0208
    1.2    2.9167
    1.3    2.8125
    1.4    2.7083
    1.5    2.6042
    1.6       2.5