Number System

Integral Solutions

Hard

If $|x| <100$ and $|y| <100$ , then the number of integer solutions of $(x, y)$ satisfying the equation $4x + 7y = 3$ is

Entered answer:

✅ Correct Answer: 29

Solution figure for IPMAT Indore 2019 SA question 16 (Number System)

Trick: You have the reduce the value of $x$ by the co-efficient of $y$ (which is 7). Similarly, $y$ is reduced by the co-efficient of $x$ (which is 4).

Watch Now

Coefficients > 1

Watch Now

General Formula

Watch Now

Solved Example (No. of Solutions)

IPMAT Indore 2023

Let $[x]$ denote the greatest integer not exceeding $x$ and { $x$ } $= x - [x]$ If $n$ is a natural number, then the sum of all values of $x$ satisfying the equation $2[x] = x + n$ { $x$ } is

IPMAT Indore 2025

If $m$ and $n$ are two positive integers such that $7m + 11n = 200$ , then the minimum possible value of $m + n$ is

IPMAT Indore 2026

The number of integer solutions $(x, y)$ of the inequality $x^2 + y^2 \leq 10$ is

If ∣x∣<100|x| <100∣x∣<100 and ∣y∣<100|y| <100∣y∣<100, then the number of integer solutions of (x,y)(x, y)(x,y) satisfying the equation 4x+7y=34x + 7y = 34x+7y=3 is

Solution

Related questions:

Keyboard Shortcuts

IPMAT Indore Past Year Questions (Topic-Wise)

If $|x| <100$ and $|y| <100$ , then the number of integer solutions of $(x, y)$ satisfying the equation $4x + 7y = 3$ is