Mathematics — first biennium · Lesson
A system solution must satisfy both equations. Geometrically it is a common point of the two lines.
Prerequisites: Equations and linear functions
Goal: Interpret a system as the intersection of two lines and classify its solutions.
In this lesson: Interpret a system as the intersection of two lines and classify its solutions.
New concept: A system of two linear equations asks for a pair (x,y) satisfying both equations. Graphically it is the intersection of two lines: one intersection gives one solution, distinct parallel lines give none, and coincident lines give infinitely many.
How to proceed: Compare coefficients: if all are proportional the lines coincide; if only x and y coefficients are proportional they are distinct parallels; otherwise they generally intersect.
You can already assume: Equations and linear functions.
Completed exercises: 0/5 · Correct on first attempt: 0
Compare coefficients: if all are proportional the lines coincide; if only x and y coefficients are proportional they are distinct parallels; otherwise they generally intersect.
Data / situation: 2x+4y=6; 4x−2y=6
ConceptStep separates what is required from what is recommended or useful as reinforcement. Only required prerequisites block your progress.
Relationships: solid line = required · dashed line = recommended · dotted line = reinforcement.