Question

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.

Answer 1

Answer:

we do not have the integer coeficients, so the solutions may not be in the range -10 to 10 (it does not happen for all coeficients) so let's do other thing:

Ok, suppose you have the equations:

1) A*x + B*y = C

2) a*x + b*y = c

where A, B, C, a, b and d are knowed.

Let's solve them in the most general way, and you always can use those solutions in the future, just need to replace the values of the constants up there.

First, we isolate x or y in a equation, let's do it with x in equation 1:

A*x  = C - B*y

x = (C - B*y)/A

Now we can replace this in the equation 2, and solve it for y:

a*x + b*y = c

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)

Now you have a solution for y, and we you know the value of y, you can put it in the eqution:

x = (C - B*y)/A

and find the value of x

Answer 2

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