Complex Elimination

Algebra 1 · Axiom Academy

Solve a system where you must scale BOTH equations to eliminate a variable. Solve the system by elimination. Neither variable's coefficients are multiples of each other, so a single multiplier won't work — you'll need to scale both equations. Key Takeaways: The Strategy for Complex Elimination Nice work — you solved a system where a single multiplier wasn't enough. The general strategy: Check what one multiplier can do: if no single equation can be scaled to match the other's coefficients, you must scale both . Pick a variable to kill: target the pair with the smaller least common multiple. Here `y`'s coefficients `3` and `2` give ` = 6`. Choose opposite multipliers: scale each equation to make those coefficients exact opposites — `+6y` and `-6y`. Add, then solve: adding eliminates the variable, leaving one equation in one unknown. Back-substitute: put that value into an original equation to find the second variable, and write the answer as an ordered pair `(x, y)`. Scaling both equations turns any linear system into one you can crack by elimination — even when the coefficients don't line up nicely.

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