Solve simple nonlinear equations in the form [A]x=b

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The discussion centers on solving simple nonlinear equations of the form [A]x=b, with specific examples provided. The equations presented are 3x = 30, x + 2y = 20, and x + yz = 15, with the known solution being (10, 5, 1). The user seeks a robust method for solving such equations without relying on numerical methods like Newton's method. They emphasize the simplicity of finding exact solutions for these particular cases. The conversation highlights the need for effective strategies in tackling nonlinear equations.
matthewjames812
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Hi! I have a simple set of nonlinear equations

1) 3x = 30

2) x+2y = 20

3) x + y*z = 15

Clearly the solution to this is (10,5,1) but I want to find a robust way to solve this type of problem [A]x=b (where [A] is a simple function of x) which doesn't involve numerically solving using Newtons method.

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But it is very trivial to solve these particular examples exactly.
 
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