Three Unknowns
Part of the Graphs & Systems section of Coddy's Algebra journey. Lesson 56 of 64.
More unknowns, same moves. With three equations, eliminate one variable to get a two-variable system, then finish as usual. In x + y + z = 6; x - y = 1; y + z = 4 the third line hands over z = 4 - y, and substituting it into the first leaves the small system x + y + (4 - y) = 6, so x = 2, then y = 1 from the second, then z = 3.
Nothing new happened: substitution and elimination simply ran twice. Systems grow in size, not in ideas.
Challenge
Solve the system x + y + z = 10; x - y = 2; z = 2y for x and y and z.
Try it yourself
Solve for x,y,z
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Graphs & Systems
1The Coordinate Plane
Two Numbers, One PointThe Four QuadrantsPoints on the AxesMirror PointsRecap: The Plane4Slope-Intercept Form
y = mx + bThe Starting HeightWrite the EquationSolve for yDraw From Any FormRecap: y = mx + b7Parallel & Perpendicular
Same Slope, Never MeetThe Perpendicular SlopeA Right-Angle LineRecap: Two Relations2From Rule to Line
A Rule Makes PointsThe Points Line UpOn the Line or Not?Between the DotsRecap: Rule to Line5Point-Slope Form
A Point and a SlopeFrom Two PointsFlat or Vertical ThroughDraw From a PointRecap: Point-Slope11Solving Systems Exactly
SubstitutionIsolate FirstEliminationScale, Then AddThree UnknownsTwo Numbers, Two FactsRecap: Two Methods