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Simplifying ax + -1ay + 2bx + -2by + 3cx + -3cy = 0 Solving ax + -1ay + 2bx + -2by + 3cx + -3cy = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2bx' to each side of the equation. ax + -1ay + 2bx + -2by + 3cx + -2bx + -3cy = 0 + -2bx Reorder the terms: ax + -1ay + 2bx + -2bx + -2by + 3cx + -3cy = 0 + -2bx Combine like terms: 2bx + -2bx = 0 ax + -1ay + 0 + -2by + 3cx + -3cy = 0 + -2bx ax + -1ay + -2by + 3cx + -3cy = 0 + -2bx Remove the zero: ax + -1ay + -2by + 3cx + -3cy = -2bx Add '2by' to each side of the equation. ax + -1ay + -2by + 3cx + 2by + -3cy = -2bx + 2by Reorder the terms: ax + -1ay + -2by + 2by + 3cx + -3cy = -2bx + 2by Combine like terms: -2by + 2by = 0 ax + -1ay + 0 + 3cx + -3cy = -2bx + 2by ax + -1ay + 3cx + -3cy = -2bx + 2by Add '-3cx' to each side of the equation. ax + -1ay + 3cx + -3cx + -3cy = -2bx + 2by + -3cx Combine like terms: 3cx + -3cx = 0 ax + -1ay + 0 + -3cy = -2bx + 2by + -3cx ax + -1ay + -3cy = -2bx + 2by + -3cx Add '3cy' to each side of the equation. ax + -1ay + -3cy + 3cy = -2bx + 2by + -3cx + 3cy Combine like terms: -3cy + 3cy = 0 ax + -1ay + 0 = -2bx + 2by + -3cx + 3cy ax + -1ay = -2bx + 2by + -3cx + 3cy Reorder the terms: ax + -1ay + 2bx + -2by + 3cx + -3cy = -2bx + 2bx + 2by + -2by + -3cx + 3cx + 3cy + -3cy Combine like terms: -2bx + 2bx = 0 ax + -1ay + 2bx + -2by + 3cx + -3cy = 0 + 2by + -2by + -3cx + 3cx + 3cy + -3cy ax + -1ay + 2bx + -2by + 3cx + -3cy = 2by + -2by + -3cx + 3cx + 3cy + -3cy Combine like terms: 2by + -2by = 0 ax + -1ay + 2bx + -2by + 3cx + -3cy = 0 + -3cx + 3cx + 3cy + -3cy ax + -1ay + 2bx + -2by + 3cx + -3cy = -3cx + 3cx + 3cy + -3cy Combine like terms: -3cx + 3cx = 0 ax + -1ay + 2bx + -2by + 3cx + -3cy = 0 + 3cy + -3cy ax + -1ay + 2bx + -2by + 3cx + -3cy = 3cy + -3cy Combine like terms: 3cy + -3cy = 0 ax + -1ay + 2bx + -2by + 3cx + -3cy = 0 The solution to this equation could not be determined.
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