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Simplifying a(3x + -1y) + b(3x + -1y) + -5(3x + -1y) = 0 (3x * a + -1y * a) + b(3x + -1y) + -5(3x + -1y) = 0 (3ax + -1ay) + b(3x + -1y) + -5(3x + -1y) = 0 3ax + -1ay + (3x * b + -1y * b) + -5(3x + -1y) = 0 3ax + -1ay + (3bx + -1by) + -5(3x + -1y) = 0 3ax + -1ay + 3bx + -1by + (3x * -5 + -1y * -5) = 0 3ax + -1ay + 3bx + -1by + (-15x + 5y) = 0 Solving 3ax + -1ay + 3bx + -1by + -15x + 5y = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3bx' to each side of the equation. 3ax + -1ay + 3bx + -1by + -15x + -3bx + 5y = 0 + -3bx Reorder the terms: 3ax + -1ay + 3bx + -3bx + -1by + -15x + 5y = 0 + -3bx Combine like terms: 3bx + -3bx = 0 3ax + -1ay + 0 + -1by + -15x + 5y = 0 + -3bx 3ax + -1ay + -1by + -15x + 5y = 0 + -3bx Remove the zero: 3ax + -1ay + -1by + -15x + 5y = -3bx Add 'by' to each side of the equation. 3ax + -1ay + -1by + -15x + by + 5y = -3bx + by Reorder the terms: 3ax + -1ay + -1by + by + -15x + 5y = -3bx + by Combine like terms: -1by + by = 0 3ax + -1ay + 0 + -15x + 5y = -3bx + by 3ax + -1ay + -15x + 5y = -3bx + by Add '15x' to each side of the equation. 3ax + -1ay + -15x + 15x + 5y = -3bx + by + 15x Combine like terms: -15x + 15x = 0 3ax + -1ay + 0 + 5y = -3bx + by + 15x 3ax + -1ay + 5y = -3bx + by + 15x Add '-5y' to each side of the equation. 3ax + -1ay + 5y + -5y = -3bx + by + 15x + -5y Combine like terms: 5y + -5y = 0 3ax + -1ay + 0 = -3bx + by + 15x + -5y 3ax + -1ay = -3bx + by + 15x + -5y Reorder the terms: 3ax + -1ay + 3bx + -1by + -15x + 5y = -3bx + 3bx + by + -1by + 15x + -15x + -5y + 5y Combine like terms: -3bx + 3bx = 0 3ax + -1ay + 3bx + -1by + -15x + 5y = 0 + by + -1by + 15x + -15x + -5y + 5y 3ax + -1ay + 3bx + -1by + -15x + 5y = by + -1by + 15x + -15x + -5y + 5y Combine like terms: by + -1by = 0 3ax + -1ay + 3bx + -1by + -15x + 5y = 0 + 15x + -15x + -5y + 5y 3ax + -1ay + 3bx + -1by + -15x + 5y = 15x + -15x + -5y + 5y Combine like terms: 15x + -15x = 0 3ax + -1ay + 3bx + -1by + -15x + 5y = 0 + -5y + 5y 3ax + -1ay + 3bx + -1by + -15x + 5y = -5y + 5y Combine like terms: -5y + 5y = 0 3ax + -1ay + 3bx + -1by + -15x + 5y = 0 The solution to this equation could not be determined.
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