The Math Meridian
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Solve systems by elimination

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Learn it Multiply one or both equations so a variable has opposite coefficients, then add to eliminate it. If the variables cancel and you get $0 = 5$, there is no solution; if you get $0 = 0$, there are infinitely many.

Example: $3x + 2y = 16$ and $5x - 4y = -10$

  1. Multiply the first by 2: $6x + 4y = 32$.
  2. Add to the second: $11x = 22$, $x = 2$.
  3. $3(2) + 2y = 16$, $y = 5$. Solution: $(2, 5)$.

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