Example Card: Solving an Inconsistent System
Identify and solve inconsistent systems of equations in Grade 9 Algebra where parallel lines yield no solution. Learn to spot false statements like 0=-2 as proof of no solution.
Key Concepts
What happens when a system of equations leads to an impossible conclusion? Let's find out with our first key idea, an inconsistent system.
Example Problem.
Solve the system: $ 5x + y = 2$ and $y = 5x$.
Common Questions
What is an inconsistent system of equations?
An inconsistent system is a set of equations with no solution because the lines are parallel and never intersect. When you solve it algebraically, all variables cancel out and you get a false statement like 0 = -2, which signals no solution exists.
How do you identify an inconsistent system using substitution?
Substitute one equation's expression into the other. If the variables disappear entirely and you're left with a false numeric statement such as 5 = -2, the system is inconsistent with no solution. The lines are parallel and do not cross.
What is the difference between an inconsistent system and a dependent system?
An inconsistent system produces a false statement (like 0 = -2) meaning no solution. A dependent system produces a true statement (like 5 = 5) meaning infinitely many solutions. These are opposite outcomes when variables cancel.