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Simplifying 3(x + -2y + -5) + -2(y + -2x + 4) = ax + by + c Reorder the terms: 3(-5 + x + -2y) + -2(y + -2x + 4) = ax + by + c (-5 * 3 + x * 3 + -2y * 3) + -2(y + -2x + 4) = ax + by + c (-15 + 3x + -6y) + -2(y + -2x + 4) = ax + by + c Reorder the terms: -15 + 3x + -6y + -2(4 + -2x + y) = ax + by + c -15 + 3x + -6y + (4 * -2 + -2x * -2 + y * -2) = ax + by + c -15 + 3x + -6y + (-8 + 4x + -2y) = ax + by + c Reorder the terms: -15 + -8 + 3x + 4x + -6y + -2y = ax + by + c Combine like terms: -15 + -8 = -23 -23 + 3x + 4x + -6y + -2y = ax + by + c Combine like terms: 3x + 4x = 7x -23 + 7x + -6y + -2y = ax + by + c Combine like terms: -6y + -2y = -8y -23 + 7x + -8y = ax + by + c Solving -23 + 7x + -8y = ax + by + c Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1ax' to each side of the equation. -23 + 7x + -1ax + -8y = ax + by + -1ax + c Reorder the terms: -23 + -1ax + 7x + -8y = ax + by + -1ax + c Reorder the terms: -23 + -1ax + 7x + -8y = ax + -1ax + by + c Combine like terms: ax + -1ax = 0 -23 + -1ax + 7x + -8y = 0 + by + c -23 + -1ax + 7x + -8y = by + c Add '23' to each side of the equation. -23 + -1ax + 7x + 23 + -8y = by + 23 + c Reorder the terms: -23 + 23 + -1ax + 7x + -8y = by + 23 + c Combine like terms: -23 + 23 = 0 0 + -1ax + 7x + -8y = by + 23 + c -1ax + 7x + -8y = by + 23 + c Reorder the terms: -1ax + 7x + -8y = 23 + by + c Add '8y' to each side of the equation. -1ax + 7x + -8y + 8y = 23 + by + c + 8y Combine like terms: -8y + 8y = 0 -1ax + 7x + 0 = 23 + by + c + 8y -1ax + 7x = 23 + by + c + 8y Reorder the terms: -23 + -1ax + -1by + -1c + 7x + -8y = 23 + by + c + 8y + -23 + -1by + -1c + -8y Reorder the terms: -23 + -1ax + -1by + -1c + 7x + -8y = 23 + -23 + by + -1by + c + -1c + 8y + -8y Combine like terms: 23 + -23 = 0 -23 + -1ax + -1by + -1c + 7x + -8y = 0 + by + -1by + c + -1c + 8y + -8y -23 + -1ax + -1by + -1c + 7x + -8y = by + -1by + c + -1c + 8y + -8y Combine like terms: by + -1by = 0 -23 + -1ax + -1by + -1c + 7x + -8y = 0 + c + -1c + 8y + -8y -23 + -1ax + -1by + -1c + 7x + -8y = c + -1c + 8y + -8y Combine like terms: c + -1c = 0 -23 + -1ax + -1by + -1c + 7x + -8y = 0 + 8y + -8y -23 + -1ax + -1by + -1c + 7x + -8y = 8y + -8y Combine like terms: 8y + -8y = 0 -23 + -1ax + -1by + -1c + 7x + -8y = 0 The solution to this equation could not be determined.
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