given 5x+22y=18 find for x,y integer


Question and Answers Forum

All Questions Topic List
Algebra Questions
Previous in All Question Next in All Question
Previous in Algebra Next in Algebra
Question Number 78233 by jagoll last updated on 15/Jan/20

$g i v e n 5 x + 22 y = 18$ $f i n d f o r x, y i n t e g e r$
Commented by mr W last updated on 15/Jan/20

$x = - 22 k + 8$ $y = 5 k - 1$ $w i t h k = a n y i n t e r g e r$
Commented by jagoll last updated on 15/Jan/20

$w h y - 22 k + 8 s i r$
Commented by jagoll last updated on 15/Jan/20

$n o t - 22 k + 18 ? s i r$
Commented by mr W last updated on 15/Jan/20

$p l e a s e r e a d t h e c o m p l e t e Q 19198 .$
Commented by jagoll last updated on 15/Jan/20

$f o r k = 0$ $x = 8, y = - 1 \Rightarrow 5 \times 8 + 22 (- 1) = 40 - 22 = 18 . r i g h t s i r$
Commented by jagoll last updated on 15/Jan/20

$o k s i r . i w i l l r e a d$
Commented by mathmax by abdo last updated on 15/Jan/20
$solution in Z^2 we consider congruence modulo 5 (Z/5Z is corps) (e) ⇒5^− x^− +22^− y^− =18^− ⇒0 +2y^− =3^− =(−2)^− ⇒y^− =(−1)^− ⇒ y=−1+5k (k integr) ⇒5x=18−22(−1+5k) =18+22−110k =40−110k ⇒x =((40−110k)/5) =8−22k ⇒ S ={(8−22k,−1+5k) /k ∈Z}$
$s o l u t i o n i n Z^{2} w e c o n s i d e r c o n g r u e n c e m o d u l o 5 (Z / 5 Z i s c o r p s)$ $Missing \left or extra \right$ $y = - 1 + 5 k (k i n t e g r) \Rightarrow 5 x = 18 - 22 (- 1 + 5 k) = 18 + 22 - 110 k$ $= 40 - 110 k \Rightarrow x = \frac{40 - 110 k}{5} = 8 - 22 k \Rightarrow$ $S = {(8 - 22 k, - 1 + 5 k) / k \in Z}$
Commented by TawaTawa last updated on 15/Jan/20

$5 x + 22 y = 18$ $Compare with : ax + by = n$ $a = 5, b = 22, n = 18$ $d = \gcd (5, 22) = 1$ $∴ Integer solution of 5 x + 22 y = 18$ $x_{0} = 8 and y_{0} = - 1$ $Therefore,$ $General solution :$ $x = x_{0} - \frac{bk}{d} and y = y_{0} + \frac{ak}{d}$ $∴ x = 8 - \frac{22 k}{1} and y = - 1 + \frac{5 k}{1}$ $∴ x = 8 - 22 k and y = - 1 + 5 k$ $with k be any integer .$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum