# 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

**Solution:**

Given: Linear equation y = 3x + 5

We kneed to find how many solutions can satisfy the given equation.

We know that,

y = 3x + 5 is a linear equation in two variables in the form of ax + by + c = 0

- For x = 0, y = 0 + 5 = 5. Therefore, (0, 5) is one solution.
- For x = 1, y = 3 × 1 + 5 = 8. Therefore, (1, 8) is another solution.
- For y = 0, 3x + 5 = 0, x = -5/3. Therefore, (-5/3, 0) is another solution.

Clearly, for different values of x, we get various values for y. Thus, any value substituted for x in the given equation will constitute another solution for the given equation. So, there is no end to the number of different solutions obtained on substituting real values for x in the given linear equation. Therefore, a linear equation in two variables has infinitely many solutions.

Thus, y = 3x + 5 has infinitely many solutions.

Hence (iii) is the correct answer.

**Video Solution:**

## 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

### NCERT Solutions Class 9 Maths - Chapter 4 Exercise 4.2 Question 1:

**Summary:**

The linear equation y = 3x + 5 has infinitely many solution as for every value of x , there is a corresponding value of y and option (iii) infinitely many solutions is the correct option.