Numerous engineering and scientific applications require finding solutions to a set of equations. Ex: 8x + 7y = 38 and 3x - 5y =

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Numerous engineering and scientific applications require finding solutions to a set of equations. Ex: 8x + 7y = 38 and 3x - 5y =

-1 have a solution x = 3, y = 2. Given integer coefficients of two linear equations with variables x and y, use brute force to find an integer solution for x and y in the range -10 to 10.

Physics

2 answers:

Softa [3K] · Answer 1 · 2026-02-21T23:47:23+03:00

Answer:

Since we lack the integer coefficients, the solutions could be outside the -10 to 10 range (this isn't the case for every coefficient). Let's proceed differently:

Assume you have the following equations:

1) A*x + B*y = C

2) a*x + b*y = c

where A, B, C, a, b, and c are known.

We will solve this in a general manner, and you can apply these solutions in the future by simply substituting the values for the constants above.

To start, we can express x in terms of y using equation 1:

A*x = C - B*y

x = (C - B*y) / A

Now, we can substitute this expression for x into equation 2 and solve for y:

a*(C - B*y)/A + b*y = c

y*(b - a*B/A) = c - a*C/A

y = (c - a*C/A) / (b - a*B/A)