Two online calculators and solvers for systems of 2 by 2 and 3 by 3 linear equations using Cramer's rule and showing the steps.

Use the Systems of Equations Solver and Calculator to Solve 2 by 2 Syatems of EquationsEnter the coefficients \( a_1, b_1, c_1, a_2, b_2 \text{ and } c2 \) as defined in the system above and the number of decimal places in the results as decimals and press "Solve System" to obtain the answer, the values of the different determinant and all steps included in the calculations.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 using different values for the coefficients. , , ,
Systems of Equations Solver and Calculator to Solve 3 by 3 Systems of EquationsBelow is a 3 by 3 system of linear equations solver where the system is of the form\[ \left\{ \begin{array}{lcl} a_1 x + b_1 y + c_1 z = & \color{red}{d_1}\\ a_2 x + b_2 y + c_2 = & \color{red}{d_2} \\ a_3 x + b_3 y + c_3 = & \color{red}{d_3} \\ \end{array} \right. \] and the solutions are given by \[ x = \dfrac{D_x}{D} , y = \dfrac{D_y}{D} , z = \dfrac{D_z}{D} \] for \( D \ne 0 \) and where \( D, D_x, D_y \text{and} D_z \) are determinants of 3 by 3 matrices defined by \( D = \begin{vmatrix}a_1&b_1&c_1\\ a_2&b_2&c_2\\a_3 & b_3 & c_3 \end{vmatrix}\) \( D_x = \begin{vmatrix}\color{red}{d_1} & b_1 & c_1\\ \color{red}{d_2} & b_2 & c_2 \\ \color{red}{d_3} &b_3&c_3 \end{vmatrix} \), \( D_y = \begin{vmatrix}a_1&\color{red}{d_1}&c_1\\ a_2&\color{red}{d_2}&c_2\\a_3 & \color{red}{d_3} & c_3 \end{vmatrix}\) , \( D_z = \begin{vmatrix}a_1&b_1&\color{red}{d_1}\\ a_2&b_2&\color{red}{d_2}\\a_3 & b_3 & \color{red}{d_3} \end{vmatrix}\) , , , , ,
More References and linksDeterminant of a Square Matrix.Cramer's Rule to Solve Systems of Equations. Solve Systems of Equations. Maths Calculators and Solvers. 