E-STAR - Student

A system of two linear equations (simultaneous linear equations) in two variables is equations that can be represented as

A solution of system of two equations in two variables, say x and y, is an ordered pair (x, y) that satisfy both equations. The set of all possible ordered pairs that satisfy both equations is called the truth set (or solution set) of the system.
A system of simultaneous linear equations can have either: one unique solution, infinitely many solutions or no solutions. In particular, considering the two lines of the two equations,
If the two lines intersect at one point, the system has one unique solution. In this case the ordered pair corresponding to the intersection point is the solution of the system.
If the two lines coincide (overlap), then the system has infinitely many solutions. I.e., the ordered pairs of every point that lie on the line are solutions of the system.
If the two lines are distinct parallel lines, then the system has no solution.