Solving system of linear equations with two variables using Cramer’s rule. In mathematics the coefficients

of linear equations are represented in the form of matrices. A matrix is a two-dimensional array in

programming. The steps of Cramer’s rule to solve the system of equations are:

Step 1: Determining the coefficient matrix from linear equations e.g.

a1x+b1y=d1

a2x+b2y=d2

Coefficient matrix: D =

Step 2: Determining the constant column C =

Step 3: Finding determinant |D| = (a1*b2) – (b1*a2) and checking if |D| is not equal to zero then do the

following:

1. Determining X-matrix: DX =

The coefficients of the x−column are replaced by the constant column

a1 b1

a2 b2

d1

d2

d1 b1

d2 b2

2. Determining Y-matrix: Dy =

The coefficients of the Y−column are replaced by the constant column

3. To solve for x: x=|DX|/|D|

4. To solve for y: y=|Dy|/|D|

Note that if |D|=0 then the matrix is singular and solving the system of equation

is not possible.

You’re required to automate all these steps by writing a program in C++ using two dimensional arrays

where required. Ask user to enter elements for coefficient matrix D and constant column C. Once the D and

C are populated you should perform all steps above and display the values for x and y to the user. Note that

in the case of a singular matrix, display a message for the system of equations can’t be solved.

Rubrics

• The elements of coefficient matrix and constant column must be taken dynamically

• Use of single structure of nested loop to find both x and y matrix

• Use of single structure of nested loop to find determinant of both x and y matrix