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Simplifying xa + yb + zc = ks Solving ax + by + cz = ks 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 = -1by + ks Combine like terms: by + -1by = 0 ax + 0 + cz = -1by + ks ax + cz = -1by + ks Add '-1cz' to each side of the equation. ax + cz + -1cz = -1by + -1cz + ks Combine like terms: cz + -1cz = 0 ax + 0 = -1by + -1cz + ks ax = -1by + -1cz + ks Divide each side by 'x'. a = -1bx-1y + -1cx-1z + ksx-1 Simplifying a = -1bx-1y + -1cx-1z + ksx-1
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