Systems of Equations Flashcards

Grade 8 · Math · Flashcards

Key vocabulary and concepts for solving systems of linear equations.

Flashcards

System of equations: A collection of two or more equations with the same set of variables
Solution of a system: An ordered pair (x, y) that makes all equations in the system true
Substitution method: Solve one equation for one variable, then substitute that expression into the other equation
Elimination method: Add or subtract the equations to remove one variable, then solve for the remaining one
Graphing method: Plot both lines; the intersection point is the solution
One solution: Lines intersect at exactly one point; the system is consistent and independent
No solution: Lines are parallel (same slope, different y-intercepts); the system is inconsistent
Infinitely many solutions: Both equations represent the same line; the system is consistent and dependent
Parallel lines: Lines with the same slope that never intersect
Coincident lines: Two lines that lie exactly on top of each other; represent the same equation
Linear equation: An equation whose graph is a straight line, typically in the form y = mx + b
Verify a solution: Substitute the (x, y) values into both original equations to confirm both are satisfied