College Algebra / Unit 9 Alg 488 worked example, 60 to 90 seconds
Solving by Addition
The idea
Solving by the addition method means scaling equations until one variable's coefficients are opposites, adding to eliminate it, solving, back-substituting, and checking the pair in both originals.
In practice
Solve 2x + 3y = 12 with 4x − 3y = 6. The y-coefficients, 3 and −3, are opposites already — no scaling needed. Add: 6x = 18, so x = 3. Back-substitute into the first: 6 + 3y = 12, so y = 2. Check the pair (3, 2) in both originals: 6 + 6 = 12 and 12 − 6 = 6. When no coefficients cooperate, multiply one or both equations first — scaling an equation by a nonzero constant changes nothing about its solutions, which is Video 133's both-sides law wearing system clothes.
Where people slip
Scale an entire equation, every term; a half-scaled equation is a different equation.
Your place on the trail
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Builds on
- Nothing. This is a starting point.
Unlocks
- Nothing yet depends on this.
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