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Find all possible ordered pairs that satisfy a linear equation

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Kathleen Horvath
Kathleen Horvath on 16 May 2021
Answered: Star Strider on 16 May 2021
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.

Answers (1)

Star Strider
Star Strider on 16 May 2021
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
X Y ___ ______ 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
.

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