# 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.

**☛ Check: **Class 9 Maths NCERT Solutions Chapter 4

**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.

**☛ Related Questions:**

- The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement. (Take the cost of a notebook to be ₹ x and that of a pen to be ₹ y).
- Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b, c in each case: i) 2x + 3y = 9.35 ii) x - y/5 -10 = 0 iii) -2x + 3y = 6 iv) x = 3y v) 2x = - 5y vi) 3x + 2 = 0 vii) y - 2 = 0 viii) 5 = 2x
- 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

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