[tex]X=n(u+t)\\X+Y=nu+ta\\Y=nu+ta-X\\Y=nu+ta-n(u+t)\\Y=nu+ta-nu-nt\\Y=ta-nt\\\boxed{Y=t(a-n)}[/tex]
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[tex]X=n(u+t)\\X+Y=nu+ta\\Y=nu+ta-X\\Y=nu+ta-n(u+t)\\Y=nu+ta-nu-nt\\Y=ta-nt\\\boxed{Y=t(a-n)}[/tex]