Yes, one can determine whether a system of linear equations has a solution just by looking at the graph of the equations
The coordinates of a point satisfy the equation of a line if the point is
On the line
If a single point satisfies the equations of two lines, the point is at the intersection of the two lines, so the lines will at that point.
This means that, each point where the two lines meet is a solution to the system of equations.
This means that if you substitute the x- and y-values of the point for x and y in the equations, both equations will be Satisfied
How to determine the solution of a graph
The solution of a graph depends on the type of graph and most times points of intersection with another graph or the x-axis (for polynomials) is the solution