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Simplifying a(x + y) + -1cz = a(-1x + y + z) (x * a + y * a) + -1cz = a(-1x + y + z) (ax + ay) + -1cz = a(-1x + y + z) ax + ay + -1cz = (-1x * a + y * a + z * a) ax + ay + -1cz = (-1ax + ay + az) Add '-1ay' to each side of the equation. ax + ay + -1ay + -1cz = -1ax + ay + -1ay + az Combine like terms: ay + -1ay = 0 ax + 0 + -1cz = -1ax + ay + -1ay + az ax + -1cz = -1ax + ay + -1ay + az Combine like terms: ay + -1ay = 0 ax + -1cz = -1ax + 0 + az ax + -1cz = -1ax + az Solving ax + -1cz = -1ax + az Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add 'ax' to each side of the equation. ax + ax + -1cz = -1ax + ax + az Combine like terms: ax + ax = 2ax 2ax + -1cz = -1ax + ax + az Combine like terms: -1ax + ax = 0 2ax + -1cz = 0 + az 2ax + -1cz = az Add '-1az' to each side of the equation. 2ax + -1az + -1cz = az + -1az Combine like terms: az + -1az = 0 2ax + -1az + -1cz = 0 Add 'cz' to each side of the equation. 2ax + -1az + -1cz + cz = 0 + cz Combine like terms: -1cz + cz = 0 2ax + -1az + 0 = 0 + cz 2ax + -1az = 0 + cz Remove the zero: 2ax + -1az = cz Combine like terms: cz + -1cz = 0 2ax + -1az + -1cz = 0 The solution to this equation could not be determined.
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