A linear equation is simply an equation involving variables/indeterminates with highest power one (or zero). For example, the equation $x=4$ is linear while $x^2=4$ is not linear but quadratic.
Linear equations take the form:
Linear equations have a set of solutions with values for the variables which solve the equation consistently. For $x=4$, the only solution for the variable x is 4 such that $4=4$. This is consistent with the definition of the equation.
A linear system is when we consider several equations to be related. A linear system has the form (where rows/equations are labeled $p_1,\ldots,p_j$)