Presumably the question concerned a PAIR of linear equations! The answer is two straight lines intersecting at the point whose coordinates are the unique solution.
there is no linear equations that has no solution every problem has a solution
In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution.
The solution of a system of linear equations is a pair of values that make both of the equations true.
It is used for solving a system of linear equations where the number of equations equals the number of variables - and it is known that there is a unique solution.
Cramer's rule is applied to obtain the solution when a system of n linear equations in n variables has a unique solution.
When (the graph of the equations) the two lines intersect. The equations will tell you what the slopes of the lines are, just look at them. If they are different, then the equations have a unique solution..
The equations are consistent and dependent with infinite solution if and only if a1 / a2 = b1 / b2 = c1 / c2.
A system of linear equations that has at least one solution is called consistent.
So, take the case of two parallel lines, there is no solution at all. Now look at two equations that represent the same line, they have an infinite number of solutions. The solution is unique if and only if there is a single point of intersection. That point is the solution.
It is a system of linear equations which does not have a solution.