Parallel but non-coincident or, in more than 2 dimensions, they are skew.
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The solution to a system is an ordered pair (x,y) where the two lines intersect.
A linear equation in two variables will not have a single solution. Its solution set is a line in the Cartesian plane. The solution to non-linear equations will depend on the equation.
If the two equations are linear transformations of one another they have the same solution.
For two linear equations, they are equations representing parallel lines. (The lines must not be concurrent because if they are, you will have an infinite number of solutions.) For example y = mx + b and y = mx + c where b and c are different numbers are two non-concurrent parallel lines. The equations have no solution. With more than two linear equations there is much more scope. Unless ALL the lines meet at one point, the system will not have a solution. So a system consisting of equations defining the three lines of a triangle, for example, will not have a solution.
One linear equation in two variable cannot be solved. It is possible to express either of the two variables in terms of the other but a solution is not possible.One linear equation in two variable cannot be solved. It is possible to express either of the two variables in terms of the other but a solution is not possible.One linear equation in two variable cannot be solved. It is possible to express either of the two variables in terms of the other but a solution is not possible.One linear equation in two variable cannot be solved. It is possible to express either of the two variables in terms of the other but a solution is not possible.