Add Cramer's rule for solving system of linear equations in two variables

matrix/system_of_linear_equation_in_2_variables.py

@@ -0,0 +1,102 @@
+"""
+Theory:-
+    https://www.mathsisfun.com/algebra/systems-linear-equations-matrices.html
+    Cramer's rule for 2x2 matrix:-
+    https://www.chilimath.com/lessons/advanced-algebra/cramers-rule-with-two-variables
+    a1x + b1y = = d1
+    a2x + b2y = = d2
+"""
+
+
+def calculate_x_and_y(eq1: list[int], eq2: list[int]) -> None:
+    """
+    Solves the system of linear equation in 2 variables.
+    :param: eq1: list of 3 numbers
+    :param: eq2: list of 3 numbers
+    :return: String of result
+    input format : [a1, b1, d1], [a2, b2, d2]
+    d_matrix = [[a1, b1], [a2, b2]]
+    d is determinant of matrix d_matrix
+    dx_matrix = [[d1, b1], [d2, b2]]
+    dx is determinant of matrix dx_matrix
+    dy_matrix = [[a1, d1], [a2, d2]]
+    dy is determinant of matrix dy_matrix
+
+    >>> calculate_x_and_y([1, 2, 3], [2, 4, 6])
+    Traceback (most recent call last):
+        ...
+    ValueError: Infinite solutions. (Consistent system)
+    >>> calculate_x_and_y([1, 2, 3], [2, 4, 7])
+    Traceback (most recent call last):
+        ...
+    ValueError: No solution. (Inconsistent system)
+    >>> calculate_x_and_y([1, 2, 3], [11, 22])
+    Traceback (most recent call last):
+        ...
+    ValueError: Please enter a valid equation.
+    >>> calculate_x_and_y([11, 2, 30], [1, 0, 4])
+    Traceback (most recent call last):
+        ...
+    ValueError: Non-Trivial Solution (Consistent system) x = 4.0, y = -7.0
+    >>> calculate_x_and_y([0, 1, 6], [0, 0, 3])
+    Traceback (most recent call last):
+        ...
+    ValueError: No solution. (Inconsistent system)
+    >>> calculate_x_and_y([0, 0, 6], [0, 0, 3])
+    Traceback (most recent call last):
+        ...
+    ValueError: Both a & b of two equations can't be zero.
+    >>> calculate_x_and_y([4, 7, 1], [1, 2, 0])
+    Traceback (most recent call last):
+        ...
+    ValueError: Non-Trivial Solution (Consistent system) x = 2.0, y = -1.0
+    >>> calculate_x_and_y([1, 2, 3], [1, 2, 3])
+    Traceback (most recent call last):
+        ...
+    ValueError: Infinite solutions. (Consistent system)
+    >>> calculate_x_and_y([2, 3, 0], [5, 1, 0])
+    Traceback (most recent call last):
+        ...
+    ValueError: Trivial solution. (Consistent system) x = 0 and y = 0
+    >>> calculate_x_and_y([0, 4, 50], [2, 0, 26])
+    Traceback (most recent call last):
+        ...
+    ValueError: Non-Trivial Solution (Consistent system) x = 13.0, y = 12.5
+    >>> calculate_x_and_y([0, 4, 50], [0, 3, 99])
+    Traceback (most recent call last):
+        ...
+    ValueError: No solution. (Inconsistent system)
+    """
+
+    # Checking if the input is valid
+    if not len(eq1) == len(eq2) == 3:
+        raise ValueError("Please enter a valid equation.")
+    elif eq1[0] == eq1[1] == eq2[0] == eq2[1] == 0:
+        raise ValueError("Both a & b of two equations can't be zero.")
+
+    # Extracting the coefficients
+    a1, b1, c1 = eq1
+    a2, b2, c2 = eq2
+
+    # Calculating the determinant of matrix d_matrix, dx_matrix and dy_matrix
+    d = a1 * b2 - a2 * b1
+    dx = c1 * b2 - c2 * b1
+    dy = a1 * c2 - a2 * c1
+
+    # Checking if the system of linear equation has a solution (Using Cramer's rule)
+    if d == 0:
+        if dx == dy == 0:
+            raise ValueError("Infinite solutions. (Consistent system)")
+        else:
+            raise ValueError("No solution. (Inconsistent system)")
+    else:
+        if dx == dy == 0:
+            raise ValueError(
+                f"Trivial solution. (Consistent system) x = {0} and y = {0}"
+            )
+        else:
+            x = dx / d
+            y = dy / d
+            raise ValueError(
+                f"Non-Trivial Solution (Consistent system) x = {x}, y = {y}"
+            )