Systems of Linear Equations Flashcards

Grade 8 · Math · Flashcards

Key terms and solution strategies for systems of linear equations.

Flashcards

System of linear equations: Two or more linear equations with the same variables solved simultaneously.
Solution to a system: An ordered pair (x, y) that makes every equation in the system true.
Substitution method: Solve one equation for a variable, substitute into the other, then solve.
Elimination method: Multiply and add/subtract equations to cancel one variable.
Graphing method: Graph both lines; the intersection point is the solution.
Consistent system: A system with at least one solution.
Inconsistent system: A system with no solution — lines are parallel.
Dependent system: A system with infinitely many solutions — lines are identical.
Parallel lines in a system: Same slope, different y-intercepts — no solution exists.
Identical lines in a system: Same slope and same y-intercept — infinite solutions.
Checking a solution: Substitute the (x, y) values back into BOTH original equations to verify both are true.
Break-even point: A real-world application of systems where cost = revenue; found by solving the system.