Linear equation in one variable
Linear equation with two variables
Scalar linear equation with one unknown
The basic form of linear scalar equations with constant coefficients a and b and the variable x is:
The solution of the equation is obtained by dividing the equation by the coefficient a.
Example: Linear equation in normal form
The solution of the equation is obtained by dividing the equation by 2.
Example: conversion to normal form
1 Forming: subtraction 2x
2 Forming: addition +4. Thus, the normal form is reached.
3 Forming: Division by 2 leads to the solution.
Example: conversion of a fraction
1 Forming: multiplication by 2x
2 Forming: subtraction 4x.
3 Forming: subtraction of 1 leads to the normal form.
4 Forming: Division by 6 gives the solution.
Example: The Unknown in fractions
1 Forming: extension to the common denominator of the first fraction by 2x
2 Forming: fractions on main denominator.
3 Forming: 2x multiplication leads to a normal form.
4 Forming: Division by 4 gives the solution.
Scalar linear equation with two unknowns
The basic form of linear scalar equations with constant coefficients a, b and c and the variables x and y is:
For a and b unequal to 0, the equation has a one-dimensional solution space. Solving the equation for y is a linear equation.
Substitution with m = a / n and b = c / b results in the line equation with the gradient m and intercept n