solve this question

is the ans 29?

4x + 7y = 3

first find one solution:

mod 4 ⇒ 7y ≡ 3 ⇒ 3y ≡ 3 ⇒ y ≡ 1 (mod 4)

take y = 1 ⇒ 4x + 7 = 3 ⇒ x = -1

so general solution:

x = -1 + 7t

y = 1 - 4t

now apply constraints:

|x| < 100 ⇒ -100 < -1 + 7t < 100

⇒ -99 < 7t < 101

⇒ -14.14 < t < 14.42

⇒ t = -14 to 14

|y| < 100 ⇒ -100 < 1 - 4t < 100

⇒ -101 < -4t < 99

⇒ -24.75 < t < 25.25

⇒ t = -24 to 25

combine both:

t = -14 to 14

number of integer values:

= 14 - (-14) + 1 = 29