MAT1791-ABED: B. Example | MoodleHUB 🎓

When trying to solve a system of linear equations that has zero or an infinite number of solutions, the result may seem odd. The following example tries to solve a system of equations representing parallel lines.

Example 1

Solve the system $y = 3 x + 1$ and $y = 3 x + 5$ by elimination.

0 = –4 is a false statement.
It will always be false, regardless of what the values of $x$ and $y$ are, so there is no solution.

Key Lesson Marker

Algebraically trying to solve a system of equations representing parallel lines results in a false statement, which tells you there is no solution. In other words, the false statement tells you that there are no values for the variables that satisfy both equations.

Algebraically trying to solve a system of equations representing coincident lines results in a true statement, which tells you there are an infinite number of solutions. In other words, the true statement tells you that any variable values that satisfy one equation will also satisfy the other.

The following video shows examples of what happens when we try to solve a system of equations with no solutions and a system of equations with infinite solutions.