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I have a set of equations that look like this:

y1 = k1*x1 + k2*x2 - A1 = 0

y2 = k3*x1 + k4*x3 - A2 = 0

y3 = k5*x2 + k6*x4 - A3 = 0

y4 = k7*x3 - A4 = 0

y5 = k8*x4 - A5 = 0

k1 to k8 are knownpositiveconstants. A1 to A5 are knownpositiveconstants (I will use different values for A1 to A5 depending on the cirumstances).

Assuming this system does not have any solution, how do I calculate the values of x1 to x4 such that y1 to y5 come as close to 0 as possible?All constants must be positive.

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# A Getting as close as possible to a solution (system of equations)?

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