A system of **linear equations** consists of two or more equations that share the same set of variables. In the case of two equations with two variables, each equation describes a line on a coordinate plane. The **solution** to the system is the point where these two lines intersect, representing the values of the variables that satisfy both equations simultaneously.

**Systems of linear equations** are commonly used in real-world scenarios such as:
- Finding the intersection point of two roads;
- Determining how two budget constraints overlap;
- Solving for unknowns in mixture and investment problems.

By solving these systems, you can answer questions like: `At what price and quantity do supply and demand curves meet?` or `How do two different payment plans compare over time?`


import unittest
import user_code
import ast
import re   
import importlib
import csv
import unittest
import importlib

class TestTask(unittest.TestCase):
    def test_unique_solution(self):
        import user_code
        importlib.reload(user_code)
        result = None
        try:
            result = user_code.solve_linear_system(2, 3, 13, 4, -2, 2)
        except Exception as e:
            _dynamic_test(
                self,
                False,
                "Function returns correct solution",
                f"Unexpected exception: {e}"
            )
            return
        expected = (2.0, 3.0)
        _dynamic_test(
            self,
            isinstance(result, tuple) and len(result) == 2 and abs(result[0] - expected[0]) < 1e-6 and abs(result[1] - expected[1]) < 1e-6,
            "Returns correct solution tuple for unique solution",
            f"Expected {expected}, got {result}"
        )

    def test_no_unique_solution(self):
        import user_code
        importlib.reload(user_code)
        raised = False
        try:
            user_code.solve_linear_system(1, 2, 3, 2, 4, 6)
        except Exception as e:
            raised = True
            _dynamic_test(
                self,
                isinstance(e, Exception),
                "Raises exception for no unique solution",
                f"Exception type not correct: {type(e)}"
            )
        _dynamic_test(
            self,
            raised,
            "Exception was raised for no unique solution",
            "No exception was raised for system with no unique solution"
        )

    def test_negative_coefficients(self):
        import user_code
        importlib.reload(user_code)
        try:
            result = user_code.solve_linear_system(-1, 2, 3, 4, -7, -10)
        except Exception as e:
            _dynamic_test(self, False, "Handles negative coefficients", f"Unexpected exception: {e}")
            return
    
        expected = (1.0, 2.0)
        _dynamic_test(
            self,
            isinstance(result, tuple) and len(result) == 2
            and abs(result[0] - expected[0]) < 1e-6
            and abs(result[1] - expected[1]) < 1e-6,
            "Correct result for negative coefficients",
            f"Expected {expected}, got {result}"
        )


    def test_zero_coefficients(self):
        import user_code
        importlib.reload(user_code)
        result = None
        try:
            result = user_code.solve_linear_system(0, 1, 4, 1, 0, 2)
        except Exception as e:
            _dynamic_test(
                self,
                False,
                "Handles zero coefficients",
                f"Unexpected exception: {e}"
            )
            return
        expected = (2.0, 4.0)
        _dynamic_test(
            self,
            isinstance(result, tuple) and len(result) == 2 and abs(result[0] - expected[0]) < 1e-6 and abs(result[1] - expected[1]) < 1e-6,
            "Correct result for zero coefficients",
            f"Expected {expected}, got {result}"
        )

    def test_zero_constants(self):
        import user_code
        importlib.reload(user_code)
        result = None
        try:
            result = user_code.solve_linear_system(1, 1, 0, 2, -1, 0)
        except Exception as e:
            _dynamic_test(
                self,
                False,
                "Handles zero constants",
                f"Unexpected exception: {e}"
            )
            return
        expected = (0.0, 0.0)
        _dynamic_test(
            self,
            isinstance(result, tuple) and len(result) == 2 and abs(result[0] - expected[0]) < 1e-6 and abs(result[1] - expected[1]) < 1e-6,
            "Correct result for zero constants",
            f"Expected {expected}, got {result}"
        )

def _dynamic_test(test_case, condition, success_message, failure_message):
    if condition:
        test_case._testMethodName = success_message
        test_case.assertTrue(True, success_message)
    else:
        test_case._testMethodName = failure_message
        test_case.fail(failure_message)

def normalize_text(text):
    text = text.lower()
    text = re.sub(r"\\s{2,}", " ", text)
    text = re.sub(r"\\s*([,:?])\\s*", r"\\1 ", text)
    return text.strip()

def change_var(code: str, var_name: str, value: str) -> str:
    tree = ast.parse(code)
    lines = code.splitlines()
    changed = False
    # Collect all assignment nodes to modify
    assign_nodes = [
        (i, node)
        for i, node in enumerate(tree.body)
        if isinstance(node, ast.Assign)
        and any(isinstance(target, ast.Name) and target.id == var_name for target in node.targets)
    ]

    # If nothing to change, return unmodified code
    if not assign_nodes:
        return code

    # Perform replacements for all matching assignments (from last to first to not break line offsets)
    for i, node in reversed(assign_nodes):
        start_line = node.lineno - 1
        line = lines[start_line]
        indent = ' ' * (len(line) - len(line.lstrip()))
        lines[start_line] = f"{indent}{var_name} = {value}"
        next_line = len(lines)
        for next_node in tree.body[i+1:]:
            if hasattr(next_node, 'lineno'):
                next_line = next_node.lineno - 1
                break
        if next_line > start_line + 1:
            lines[start_line+1:next_line] = []
        changed = True

    return '\\n'.join(lines) if changed else code

if __name__ == "__main__":
    unittest.main()


test_main.py

A practical course designed for math students to harness the power of Python for solving mathematical problems, visualizing data, and applying computational thinking to real-world scenarios. Each section blends engaging theory with hands-on challenges, focusing on mathematical applications and problem-solving. 

Explore how Python can be used to perform numerical calculations, solve algebraic equations, and automate mathematical processes.

Learn how to visualize mathematical data and functions using Python, and apply these skills to real-world mathematical problems.

Apply Python to probability, statistics, and simulation, enabling students to model uncertainty and analyze data in mathematical contexts.

Challenge: Solve a System of Two Linear Equations

解答