Isolate First
Part of the Graphs & Systems section of Coddy's Algebra journey. Lesson 55 of 64.
Sometimes neither equation has a variable alone on one side. Then you isolate a variable first, and substitute after that. In the system x - y = 1; 2x + y = 8, add y to both sides of the first equation to get x = y + 1. Replace x in the second equation with y + 1: 2(y + 1) + y = 8. Expand and collect the terms to get 3y = 6, so y = 2. Then x = 2 + 1, so x = 3.
When possible, isolate a variable with coefficient 1 or -1. This avoids introducing fractions during that step. Isolating the variable in 2x also works, but requires dividing the other terms by 2.
Challenge
MediumSolve 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