given-5x-22y-18-find-for-x-y-integer-

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

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 .