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I am trying to solve equation:

Solve[{y1 == -a*Exp[-b*x1], y2 == -a*Exp[-b*x2]}, {a, b}]

using Solve method but I receive error: Solve::ivar: E^kb t is not a valid variable.I am not reallty sure why I receive this kind of error and how can I make mathematica solve this equation.

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    $\begingroup$ Maybe you had a prior definition such as a=t*Exp[kb]? $\endgroup$ – Daniel Lichtblau Mar 2 '18 at 19:10
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The following works.

Solve[{y1 == -a*Exp[-b*x1], y2 == -a*Exp[-b*x2]}, {a, b}, Reals]

{{a->ConditionalExpression[-y1 (y1/y2)^(-(x1/(x1-x2))),(y1>0&&y2>0)||(y1<0&&y2<0)],b->ConditionalExpression[-(Log[y1/y2]/(x1-x2)),(y1>0&&y2>0)||(y1<0&&y2<0)]}}

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