Linear equation

First-degree equations, i.e., equations whose variables have exponents of degree not higher than the first, are also called linear equations because, when they have two unknowns, the set of their solutions forms a straight line in the Cartesian plane

The standard or canonical form of a linear equation is:

in which 𝑎 and 𝑏 are coefficients, that is, known numbers, and 𝑥 is a variable, i.e., the placeholder of a quantity that can take on multiple values. The 𝑥, for which the exponent 1 is implied (𝑥¹), is also the unknown or the quantity you want to know the value of by solving the equation.

In the most common case, in which 𝑎≠0, the equation has only one solution:

Linear equations with two unknowns

The standard form of a linear equation with two unknowns is:

where 𝑎, 𝑏 and 𝑐 are coefficients and 𝑥 and 𝑦 the unknown variables.

These equations have pairs of solutions — one for 𝑥 and the other for 𝑦 — which we can consider as the coordinates of a point in the Cartesian plane. All the points described by the infinite pairs of solutions of a first-degree equation with…