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Question Number 192992 by gatocomcirrose last updated on 01/Jun/23

{ ((2x+3y≡1(mod26))),((7x+8y≡2(mod26))) :}

{2x+3y≡1(mod26)7x+8y≡2(mod26)

Answered by MM42 last updated on 01/Jun/23

2x+3y=26k+1 & 7x+8y=26k′+2 ⇒5x=26k′′−2⇒x≡^(26) 10 ✓ ⇒2x+3y≡^(26) 20+3y≡^(26) 1⇒3y≡^(26) −19≡7 ⇒27y≡^(26) 63≡^(26) 11⇒y≡^(26) 11 ✓

2x+3y=26k+1&7x+8y=26k′+2⇒5x=26k″−2⇒x≡2610✓⇒2x+3y≡2620+3y≡261⇒3y≡26−19≡7⇒27y≡2663≡2611⇒y≡2611✓

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