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Simplifying ax + by + cz = 1 Solving ax + by + cz = 1 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1by' to each side of the equation. ax + by + -1by + cz = 1 + -1by Combine like terms: by + -1by = 0 ax + 0 + cz = 1 + -1by ax + cz = 1 + -1by Add '-1cz' to each side of the equation. ax + cz + -1cz = 1 + -1by + -1cz Combine like terms: cz + -1cz = 0 ax + 0 = 1 + -1by + -1cz ax = 1 + -1by + -1cz Divide each side by 'x'. a = x-1 + -1bx-1y + -1cx-1z Simplifying a = x-1 + -1bx-1y + -1cx-1z Reorder the terms: a = -1bx-1y + -1cx-1z + x-1
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