Adding Equations

Algebra 1 · Axiom Academy

Two balanced scales, added together, can make an unknown disappear — the whole idea behind solving systems by elimination. A balanced scale is a true equation: whatever sits on the left weighs exactly what sits on the right. When you have two of them — two equations about the same mystery objects — you can pour both onto one bigger scale at once , and it stays balanced. If the same object shows up on both sides of that combined scale, it cancels. One unknown vanishes, and the other is suddenly easy to read. Watch the two balanced scales slide together and add. A single block sits on both sides of the combined scale, so we lift one off each side — they cancel. What's left tells us, in one clean step, the weight of an apple. Adding the two equations is exactly this: line them up, combine, and let the matching term cancel. When nothing cancels yet — scale one equation first Often the two equations don't line up so neatly. Here adding straight away leaves a leftover y . But you're allowed to multiply a whole equation by any number before adding — the scale stays balanced. Drag k to scale the second equation, and watch the y on the two sides shrink toward each other. Land the value that makes y vanish. At k = 2 the combined equation is 6x = 24 — one variable, solved. You choose which unknown disappears

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