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This equation solves a system of simultaneous linear equations in two variables using Cramer's Rule.
The two equations solved for here are of the form:
`a_1 * x + b_1 *y = c_1`
`a_2 * x + b_2 *y = c_2`
This equation returns the solution value for x.
Inputs
- `a_1` - the coefficient of the x term in the first equation
- `b_1` - the coefficient of the y term in the first equation
- `c_1` - the solution term in the first equation
- `a_2` - the coefficient of the x term in the second equation
- 'b_2` - the coefficient of the y term in the second equation
- `c_2` - the solution term in the second equation
Derivation
Given a system of simultaneous equations:
`a_1 * x + b_1 *y = c_1`
`a_2 * x + b_2 *y = c_2`
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` determinants as:
`D_x = |[c_1,b_1],[c_2,b_2]|` and
Continuing with Cramer's Rule, we compute the solution for x as:
`x = D_x/D`
