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## 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

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

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