Isolate First
Part of the Graphs & Systems section of Coddy's Algebra journey. Lesson 53 of 64.
When nothing stands alone yet, one small solve sets substitution up. In x - y = 1; 2x + y = 8 the first equation isolates x in one move, x = y + 1, and the second becomes 2(y + 1) + y = 8, so 3y = 6 and y = 2, then x = 3.
Choose the cheapest isolation on offer: a variable with coefficient 1 (or -1) comes free without fractions. Isolating the 2x instead would work, but it drags a fraction through every later line.
Challenge
Solve the system x - y = 2; 3x + y = 10 for x and y.
Try it yourself
Solve for x,y
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