decide if the equation 133x 203y28 hasa solution If yes fin

decide if the equation 133x + 203y=28 has,a solution. If yes find the solution with the smallest possible x greater than or equal to 0

please help I ended up with x= -12 but is not greater than 0

Solution

Yes, the eqn in the question has a solution.

In the question, does the question ask if x and y have to be integers? If yes, then the following is the smallest possible value for x>=0:

133x+203y=28 can be rearranged as y=(28-133x)/203 .....(eqn1)

Since x>=0 as per the question, we have the smallest value of x=17 for (eqn1) to satify. Substituting 17 in equ1 will result in a y as -11, an integer