Two Equations Two Unknowns

Geometrically, we can visualize the situation of two equations in two unknowns as the equations of two line. Typically, these lines intersect in a point that is the solution of the system. In this example, the lines 4x + 3y = 2 and 3x + 2y = 1 intersect at the point(-1, 2), which is the solution.

Possible Solution Sets: Zero, One or Infinitely Many

The system may have zero solutions if the two lines are parallel. In this case, they never intersect. In the second and most common case, the system has one solution; this happens whenever the equations do not have the same slope. In the third case, there an infinite number of solutions when the two equations describe the same line.