Question

How to solve three equations with three variable by determinants?

Answer 1

Make sure that you follow the formula on how to find the determinant of a 3×3 matrix carefully, as shown above. More so, don’t rush when you perform the required arithmetic operations in every step. This is where common errors usually occur, but it can be prevented.

$\huge \mathfrak{steps:}$

1) The coefficients of variables x, y and z make use of subscripted a, b, and c, respectively. While the constant terms use subscripted d.

2) The denominators to find the values of x , y and z are all the same which is the determinant of the coefficient matrix (coefficients coming from the columns of x, y, and z).

3) To solve for x, the coefficients of x-column is replaced by the constant column

4) To solve for y, the coefficients of y-column is replaced by the constant column

5) In the same manner, to solve for z, the coefficients of z-column is replaced by the constant column

$\huge \mathfrak{hope \: it \: helps}$