Find the solutions of each of the following systems of linea
Find the solutions of each of the following systems of linear congruences.
(a)2x+3y ?5 (mod11), x+5y ?6 (mod11)
b)4x+y ?5 (mod11), x+3y ?4 (mod11)
Solution
a). consider x=y=1 then 2(1)+3(1)=5 =5 (mod11)
(1)+5(1)=6 =6 (mods11)
so (1,1) is soultion of linear congurences in (a)
b). similarly consider x=y=1 then 4(1)+(1)=5 =5 (mod11)
(1)+3(1)=4 =4 (mods11)
so (1,1) is soultion of linear congurences in (b)
