The solutions of a linear equation form a line in the Euclidean plane, and, conversely, every line can be viewed as the set of all solutions of a linear equation in two variables.
This is the origin of the term linear for describing this type of equations.
This article considers the case of a single equation with coefficients from the field of real numbers, for which one studies the real solutions.
All of its content applies to complex solutions and, more generally, for linear equations with coefficients and solutions in any field.
Water officials expect 760 acre-feet of snowmelt from the water.
Say it’s springtime and Irene wants to fill her swimming pool.For the case of several simultaneous linear equations, see system of linear equations.There are other forms for a linear equation (see below), which can all be transformed in the standard form with simple algebraic manipulations, such as adding the same quantity to both members of the equation, or multiplying both members by the same nonzero constant.So, for this definition, the above function is linear only when are not both zero.Conversely, every line is the set of all solutions of a linear equation.are the coefficients, which are often real numbers.The coefficients may be considered as parameters of the equation, and may be arbitrary expressions, provided they do not contain any of the variables.The melt comes from a big valley, and every year the district measures the snowpack and the water supply.It gets 60 acre-feet from every 6 inches of snowpack.The solutions of such an equation are the values that, when substituted for the unknowns, make the equality true.In the case of just one variable, there is exactly one solution (provided that .