Solve the linear congruence x+2y -= 1(mod 5) 2x+y -= 1(mod 5)

geduiwelh 2021-02-05 Answered
Solve the linear congruence
x+2y1(mod5)
2x+y1(mod5)
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Expert Answer

Latisha Oneil
Answered 2021-02-06 Author has 100 answers
Step 1
Given a system of linear congruences
x+2y1(mod5)
2x+y1(mod5)
Solve it.
Step 2
Multiply the first congruence by 2.
2x+4y2(mod5)
Add the preceding one with the second congruence in the system.
4x+5y3(mod5)
4x3(mod5)
Step 3
Multiply the congruence by 41(mod5)=4 to get
16x12(mod5)
x2(mod5)
Step 4
Plugging back in x for the second equation.
4+y1(mod5)
y3(mod5)ory2(mod5)
Thus the solution of the system of congruences is
x2(mod5),y2(mod5)
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