Solve Linear Equations using eval() in Python

Linear equations using one variable of the form a + bx = c + dx can be solved in Python using eval() function. The input type will be a linear equation in the form of a string. 

Syntax:

eval(expression, globals=None, locals=None)

Here, we will transform the equation into an expression of real and imaginary numbers such that eval can easily process it.

For example, 5x + 4 = 2x + 10 becomes 5j + 4 – (2j + 10) by shifting all the terms on the right side to the left. We are transforming this equation into a complex equation because eval() is unable to otherwise process the equations. Transforming it into a complex number helps in faster evaluation. 

Step 1: We will use the replace() in python to replace “=” with “-(” and replace “x” with “j”.

Step 2: The string is then added with “+)” to complete the expression.

Step 3: Then { “j” : 1j} is done to change the equation into a format that can be easily evaluated by the eval() function. In this step all the constant terms are evaluated and the x terms or the imaginary terms as well.

Step 4: Then the evaluated expression is simply broken down into the real and imaginary parts. If the imaginary part exists or the x is true and not zero the answer is printed else if the imaginary part is 0 and the real part is true there is no solution or else there are infinite solutions. Here,

x = 2.000000

is the final solution.

Example 1:

Python3

def solve(equation):

    # replacing all the x terms with j
    # the imaginary part
    s1 = equation.replace('x', 'j')

    # shifting the equal sign to start
    # an opening bracket
    s2 = s1.replace('=', '-(')

    # adding the closing bracket to form
    # a complete expression
    s = s2+')'

    # mapping the literal j to the complex j
    z = eval(s, {'j': 1j})
    real, imag = z.real, -z.imag

    # if the imaginary part is true return the
    # answer
    if imag:
        return "x = %f" % (real/imag)
    else:
        if real:
            return "No solution"
        else:
            return "Infinite solutions"


equation = "2+3x=5x-7"
print(solve(equation))

Output

x = 4.500000

Example 2:

Python3

def solve(equation):

    # replacing all the x terms with j
    # the imaginary part
    s1 = equation.replace('x', 'j')

    # shifting the equal sign to start
    # an opening bracket
    s2 = s1.replace('=', '-(')

    # adding the closing bracket to form
    # a complete expression
    s = s2+')'

    # mapping the literal j to the complex j
    z = eval(s, {'j': 1j})
    real, imag = z.real, -z.imag

    # if the imaginary part is true return the
    # answer
    if imag:
        return "x = %f" % (real/imag)
    else:
        if real:
            return "No solution"
        else:
            return "Infinite solutions"


equation = "x=x+10"
print(solve(equation))

Output

No solution

Example 3:

Python3

def solve(equation):

    # replacing all the x terms with j
    # the imaginary part
    s1 = equation.replace('x', 'j')

    # shifting the equal sign to start
    # an opening bracket
    s2 = s1.replace('=', '-(')

    # adding the closing bracket to form
    # a complete expression
    s = s2+')'

    # mapping the literal j to the complex j
    z = eval(s, {'j': 1j})
    real, imag = z.real, -z.imag

    # if the imaginary part is true return the
    # answer
    if imag:
        return "x = %f" % (real/imag)
    else:
        if real:
            return "No solution"
        else:
            return "Infinite solutions"


equation = "2x=2x"
print(solve(equation))

Output

Infinite solutions