# How to solve simultaneous equation

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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 Edit

- Evaluate one of the variables over other variables
- Substitute the variable in the next equation by the evaluated variable

## Using Maple 10Edit

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 1Edit

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:

x_{1} = -23/10, y_{1}=-sqrt(161)/10

x_{2} = -23/10, y_{1}=+sqrt(161)/10

### Method 2Edit

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]);