The Cramer's Rule Calculator for Two Equations solves a two formula system of simultaneous linear equations in two variables using Cramer's Rule. The two equations solved for here are of the form:
INSTRUCTIONS: Enter the following:
The calculator returns the values for x and y (e.g. [1,-1] respectively).
Given a system of simultaneous equations:
a1 • x + b1 • y = c1
a2 • x + b2 • y = c2
We can represent these two equation in matrix form using a coefficient matrix, as `[[a_1,b_1],[a_2,b_2]] [[x],[y]] = [[c_1],[c_2]]`, where we refer to `[[a_1,b_1],[a_2,b_2]]` as the coefficient matrix.
Using Cramer's rule we compute the determinants of the coefficient matrix: `D = |[a_1,b_1],[a_2,b_2]| = a_1*b_2 - b_1*a_2`
We also form the `D_x` and `D_y` determinants as:
`D_x = |[c_1,b_1],[c_2,b_2]|` and
`D_y = |[a_1,c_1],[a_2,c_2]|`
Continuing with Cramer's Rule, we compute the values of x and y as:
`x = D_x/D`
`y = D_y/D`