Question:medium

Which one of the following options is true, and why? y = 3x + 5 has 

(i) a unique solution, 

(ii) only two solutions, 

(iii) infinitely many solutions

Updated On: Jan 20, 2026
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Solution and Explanation

Let's evaluate the possible solutions for the equation \( y = 3x + 5 \):

(i) a unique solution:

This is incorrect because the equation \( y = 3x + 5 \) represents a straight line. For any value of \( x \), there will be a corresponding unique value of \( y \). Therefore, the equation does not represent just one solution; it represents a relationship where for each \( x \), there is exactly one \( y \).

(ii) only two solutions:

This is incorrect because a linear equation of the form \( y = mx + b \) represents an infinite number of solutions. For each value of \( x \), you can find a corresponding value of \( y \), meaning there are more than just two solutions.

(iii) infinitely many solutions:

This is correct because the equation \( y = 3x + 5 \) represents a straight line, and a straight line contains infinitely many points. For each possible value of \( x \), there will be a corresponding \( y \), which gives an infinite number of solutions.

Answer:

(iii) infinitely many solutions.

This is because a linear equation in two variables has infinitely many solutions. For every value of \( x \), there is a corresponding value of \( y \), and this relationship is represented by a straight line on the Cartesian plane.

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Top Questions on Linear Equations

Questions Asked in CBSE Class IX exam

(Street Plan) : A city has two main roads which cross each other at the centre of the city. These two roads are along the North-South direction and East-West direction.

All the other streets of the city run parallel to these roads and are 200 m apart. There are 5 streets in each direction. Using 1cm = 200 m, draw a model of the city on your notebook. Represent the roads/streets by single lines. There are many cross- streets in your model. A particular cross-street is made by two streets, one running in the North - South direction and another in the East - West direction. Each cross street is referred to in the following manner : If the 2nd street running in the North - South direction and 5th in the East - West direction meet at some crossing, then we will call this cross-street (2, 5). Using this convention, find: 

(i) how many cross - streets can be referred to as (4, 3). 

(ii) how many cross - streets can be referred to as (3, 4).

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