How to solve a linear equation

A linear equation is an equation, both parts of which can be expressed by polynomials (from unknowns) of the first degree. A linear equation can be reduced to the form: ax + b = 0. The number of solutions of the linear equation depends on the parameters a and b.

Instruction manual

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If a = b = 0, then the equation has an infinite number of solutions, since 0 * x = 0 will hold for any x.

If a = 0, and b? 0, then the equation has no solutions. Indeed, the equality 0 * x + b = 0 is impossible for b? 0.

If a? 0, and b? 0, then the equation has a unique solution, which can be found by the formula x = -b / a.

Example:

The linear equation is given: 4x - 5 = 0, i.e. a = 4? 0; b = -5? 0.

The equation has a unique solution.

Using the formula, we find the root of the linear equation:

x = - (- 5) / 4 = 5/4 = 1.25.

So, the solution to the linear equation 4x - 5 = 0 is the number 1.25.

Indeed, 4 * 1.25 = 5.