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Key Concepts

# Key Concepts - *Key Concepts A system of equations is a SET...

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**Key Concepts** A system of equations is a SET of equations. A solution satisfies every equation in the set. For two variables: x and y . The 2 linear equations represent 2 lines in a plane. Possible solutions: . Graph: Two lines intersect at exactly one point. Solution = intersection point (x, y). System is called consistent. Equations are called independent. . Graph: Two parallel lines intersecting at no point. No solution. Solution set = Ø. System is called inconsistent. Equations are called independent. . Graph: Two lines overlap as the same line. Solution = an infinite number of intersection points. Write solution with one variable arbitrary. System is called consistent. Equations are called dependent.

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Substitution Method: . Isolate 1 variable in 1 equation. . Substitute into 2nd equation. Elimination Method: . the coefficients of the eliminated variable in two equations must be additive inverses . multiply one or both equations by a number if needed . add equations to eliminate one variable For three variables: x, y, and z . The 3 linear equations represent planes in a 3D space.
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