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)

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)Solutiona). co

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