Given the equation $$x+y=0$$ it is said that it is a linear equation with $$2$$ unknowns $$(x,y)$$ and linear because there are not quadratic or higher terms.
This equation does not have a unique solution, meaning that there are more than one combination of values of $$x$$ and $$y$$ that satisfy the equation.
Possible solutions are: $$(1,-1), (2,-2), (100,-100)$$, etc.
The equation:
$$$x+y+3t-z=2$$$
is also a linear equation, although now we have $$4$$ unknowns.
Obviously it does not have a unique solution either.
More generally, a linear equation with $$n$$ unknowns is defined as follows:
$$$a_1x_1+a_2x_2+a_3x_3+\ldots+a_nx_n=b$$$
where:
- $$a_1,a_2,\ldots,a_n$$ are called the coefficients.
- $$x_1,x_2,\ldots,x_n$$ are the unknowns.
- $$b$$ is the constant term.
It is said, also, that two equations are equivalent when they have the same solution.
The equation $$3x+3y=0$$, for example, is equivalent to $$x+y=0$$.