The Whole Truth About Whole Numbers by Sylvia Forman & Agnes M. Rash

Author:Sylvia Forman & Agnes M. Rash
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Solution

First, gcd(12, 20) = 4, so we are looking for an integer solution to the equation 12x + 20y = 4. In algebra, you may have learned techniques for solving linear equations in one variable and systems of two linear equations in two variables, but right now we do not have a systematic way to solve this equation. Before continuing, see if you can find a solution on your own.

To start looking for an integer solution, first notice that since 4 is less than both 12 and 20, either x or y will be negative. Since 12(2) = 24 which is four more than 20, x = 2, y = − 1 is a solution to the equation. Notice that x = − 3, y = 2 is also a solution (Since this is a linear equation with two variables, the solution is not unique). To test other possible solutions, substitute the values for x and y into the original equation to see if they make it true.

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