The operation Integer on the Solve submenu finds integer solutions to equations and systems of equations.
Solve + Integer
3x + 4y = 10, Solution is :x = 4N1 -10, y = - 3N1 + 10
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Thus, one solution is given by x = - 10 and y = 10, and every solution is of the form x = 4N1 - 10 and y = - 3N1 + 10, where N1 is any integer. As a check, note that, if x = 4N1 - 10 and y = - 3N1 + 10, then x + 4y = 3(4N1 -10) + 4(- 3N1 + 10) = - 30 + 40 = 10.
In a similar manner, a system of equations can be solved for integer solutions.
Solve + Integer
, Solution is :
3x + 2y = 5 3x - z = 1 x = 5 - 2N1, y = - 5 + 3N1, z = - 6N1 + 14
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Indeed, if x, y, and z are given by the stated equations, then, for
any integer N1, we have
3x + 2y = 3(5 - 2N1) + 2 -5 + 3N1
= 5
and
3x - z = 3
5 - 2N1
-
-6N1 + 14
= 1.