Hello how to solve this equation: { ((3x−y≡1[5])),((x+2y≡0[5])) :}


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Question Number 121567 by mathocean1 last updated on 09/Nov/20

$Hello how to solve this$ $equation :$ ${\begin{cases} 3 x - y \equiv 1 [5] \\ x + 2 y \equiv 0 [5] \end{cases}$
Commented by TANMAY PANACEA last updated on 09/Nov/20

$[5] w h a t d o e s [.] m e a n s$
Commented by mathocean1 last updated on 09/Nov/20

$modulo$
	Answered by mr W last updated on 11/Nov/20

	$3 x - y = 5 k + 1$ $6 x - 2 y = 10 k + 2$ $x + 2 y = 5 h$ $7 x = 5 (2 k + h) + 2$ $7 (x - 1) = 5 (2 k + h - 1)$ $\Rightarrow x = 5 n + 1$ $\Rightarrow y = 15 n - 5 k + 2$
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