 # Analytical Solvers

Numbering the entered equations:

Reorganizing the system:
 52X1 + 32X2 + 3X3 = 854 ... 6 Same as 3 2X1 - 32X2 + 3X3 = 252 ... 7 Same as 4 5X1 - X2 + 2X3 = 2 ... 8 Same as 5 X1 + 72X2 + X3 + 2X4 - 2X5 = -3 ... 9 Same as 2 X1 + X2 + 4X3 - 12X4 - 2X5 = 17 ... 10 Same as 1

Eliminating variable X1 from equation 6 and 7
We have,
 52X1 + 32X2 + 3X3 = 854 2X1 - 32X2 + 3X3 = 252

Multiplying the first and second equations by -2 and 52 respectively we get,

Adding these two equations we get,

Eliminating variable X1 from equation 7 and 8
We have,
 2X1 - 32X2 + 3X3 = 252 5X1 - X2 + 2X3 = 2

Multiplying the first and second equations by -5 and 2 respectively we get,

Adding these two equations we get,

Eliminating variable X2 from equation 11 and 12
We have,
 -274X2 + 32X3 = -454 112X2 - 11X3 = -1172

Multiplying the first and second equations by -112 and -274 respectively we get,

Adding these two equations we get,

Solving equation 13 for variable X3 we get,
Substituting the value of variable X3 from equation 14 into 11 we get,
Substituting the value of variables X3 and X2 from equations 14 and 15 into 6 we get,

Substituting the value of variables X3, X2 and X1 from equations 14, 15 and 16 into 9 and 10 we get,

Eliminating variable X4 from equation 17 and 18
We have,
 -2X4 + 2X5 = 42722 12X4 + 2X5 = 53544

Multiplying the second equation by 4 we get,

Adding these two equations we get,