How to solve simultaneous equation

simultaneous equation can be solve for by hand or using computers.

the examples below will use the following equations
 * equation 1: (x+3)^2 + (y-1)^2 = 25
 * equation 2: (x-2)^2 + (y+4)^2 = 9
 * solve for: x, y

Substitution method

 * 1) Evaluate one of the variables over other variables
 * 2) Substitute the variable in the next equation by the evaluated variable

Using Maple 10
Maple 10 is an advanced mathematical computational program used for solving and performing math based simulations  Maple can easily be used to solve simultaneous equations.

Method 1
Substitution by hand:

restart; eq1 := (x+3)^2 + (y-1)^2 = 25; solve(eq1);

We get that x = -3+sqrt(24-y^2+2*y), so we write the second equation substituting x with the expression by hand, and repeat the solve function:

eq2 := ( (-3+sqrt(24-y^2+2*y)) -2)^2 + (y+4)^2 = 9 solve(eq2);

We get the answer: x1 = -23/10, y1=-sqrt(161)/10 x2 = -23/10, y1=+sqrt(161)/10

Method 2
Alternatively, one may use the solve function to solve both equations simultaneously, using a single command:

solve({2*x - 6*y + 3 = 0, 3*y^2 - 6*x + 6 = 0}, [x, y]);

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