# Solve Systems of Equations - Calculator

Two online calculators and solvers for systems of 2 by 2 and 3 by 3 linear equations.

## Review

2 by 2 systems of linear equations are of the form
a x + b y = c
d x + e y = f
The calculator uses Cramer's rule
x = (c e - f b) / D and y = (a f - d c) / D
to solve the system.
D is the coefficient determinant given by D = a e - b d.

## How to use the calculator

### 2 by 2 Systems of Equations

Enter the coefficients a, b, c, d, e, f and the number of decimal places in the results as real number and press "enter".
This tool can be used to check the solutions of a 2 by 2 system of equations solved by hand. It can also be used, efficiently, to explore 2 by 2 system of equations.

 a = 1 b = 2 c = 3 d = 1 e = 6 f = 5 Decimal Places = 3 x = y =

### 3 by 3 Systems of Equations

Below is a 3 by 3 system of linear equations solver where the system is of the form
a x + b y + c z = k
d x + e y + f z = l
g x + h y + i z = m

 a = 1 b = 2 c = -3 k = 9 d = 1 e = 6 f = 5 l = -1 g = 1 h = 6 i = 4 m = 3 Decimal Places = 3 x = y = z =