A typical example is the system \[\lineqs{6 x^2- y^2 &=& 14 \cr 2 x^2 + 3y^2 &=& 18 \cr}\] with unknowns #x# and #y#, that can also be written as \[{6\cdot x^2- y^2 = 14 \quad \land\quad 2 x^2 + 3 y^2 = 18 }\].

In the input field of exercises, this system is entered as \[\left[6x^2-y^2 = 14, 2x^2+3y^2 = 18\right]\] .

If the order of the unknowns is defined as #[x,y]#, then the list #\left[\sqrt{3},2\right]# is a solution. To see that this is a solution, we enter #x=\sqrt{3}# and #y=2# in the equations:\[\lineqs{6\cdot 3- 4 &=& 14 \cr 2\cdot 3 + 3\cdot 4 &=& 18 \cr}\]

These equalities are true, hence #[x,y]=\left[\sqrt{3},2\right]# is a solution. To solve this system, is to find all solutions. In thise case, these are, next to the found solution: #\left[\sqrt{3},-2\right]#, #\left[-\sqrt{3},2\right]# en #\left[-\sqrt{3},-2\right]#.

The definition of equivalent coincides, in case the system consists of a single equation with one unknown, with the definition in the chapter Linear equations with one unknowns.