The document discusses finding the number of positive integer solutions (x, y) for the linear equation 2x + 5y = 103. By rearranging the equation, it is shown that y can take on 10 integer values, which correspond to 10 integer values for x. The total number of positive integer solutions is thus 10.

1. Linear Equation

2. Linear Equation
2x + 5y = 103. Find the number of positive integers, x, y, that satisfy
this equation.
(a) 9 (b) 10
(c) 12 (d) 20

3. Linear Equation
Rearranging the equation, we get.
2x = 103 – 5y
This says that when you subtract a multiple of 5 from 103, you get an
even number. You have to subtract an odd multiple of 5 from 103 in
order to get an even number. There are 20 multiples of 5 till 100, ten
of which are odd. (Note that you cannot subtract 105, or higher
multiples as they result in a negative value for x.)
2x + 5y = 103. Find the number of positive integers, x, y, that satisfy
this equation.

4. Linear Equation
So, y can have ten integer values. x also has 10 integer values, each
corresponding to a particular value of y.
y = 1, gives us a potential value for x, so do y = 3, 5, 7….19. y can take
10 values totally.
Answer choice (b)
2x + 5y = 103. Find the number of positive integers, x, y, that satisfy
this equation.

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