System of linear equations
... are inconsistent. Adding the first two equations together gives 3x + 2y = 2, which can be subtracted from the third equation to yield 0 = 1. Note that any two of these equations have a common solution. The same phenomenon can occur for any number of equations. In general, inconsistencies occur if th ...
... are inconsistent. Adding the first two equations together gives 3x + 2y = 2, which can be subtracted from the third equation to yield 0 = 1. Note that any two of these equations have a common solution. The same phenomenon can occur for any number of equations. In general, inconsistencies occur if th ...
The computational-Type Problems 1 Solving Linear Diophantine
... example, to solve 6x ≡ 8 (mod 10), notice that gcd(6, 10) = 2, then by dividing 2 on both sides, we get 3x ≡ 4 (mod 5). In other words, to solve 6x ≡ 8 (mod 10), we can instead to solve 3x ≡ 4 (mod 5). Note that now gcd(3, 5)=1, so we can used the above ”naive” method above. Note that the solution ...
... example, to solve 6x ≡ 8 (mod 10), notice that gcd(6, 10) = 2, then by dividing 2 on both sides, we get 3x ≡ 4 (mod 5). In other words, to solve 6x ≡ 8 (mod 10), we can instead to solve 3x ≡ 4 (mod 5). Note that now gcd(3, 5)=1, so we can used the above ”naive” method above. Note that the solution ...