**Assertion and Reason Questions for Class 9 Maths Chapter 4 Linear Equations in Two Variables**

** Directions: **In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).

(C) Assertion (A) is true but reason (R) is false.

(d) Assertion (A) is false but reason (R) is true.

**Q.1. Assertion :** There are infinite number of lines which passes through (3, 2).**Reason:** A linear equation in two variables has infinitely many solutions.

## Answer

Answer: (b)We know that a linear equation in two variables has infinitely many solutions. So, Reason is correct.

Through a point infinite lines can be drawn.

Through (3, 2) infinite number of lines can be drawn.

Hence, Assertion is also correct.

But reason (R) is not the correct explanation of assertion (A).

Correct option is (b)

**Q.2. Assertion :** If x = 2, y = 1 is a solution of the equation 2x + 3y = k, then the value of k is 7.**Reason:** The solution of the line will satisfy the equation of the line.

## Answer

Answer: (a)We know that the solution of the line will satisfy the equation of the line.

So, Reason is correct.

Since x = 2, y =1 is a solution of the given linear equation, we have

2×2 + 3×1 – k = 0 = 4+3 – K= 0 = K =7.

So, Assertion is also correct.

Correct option is (a)

Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

**Q.3. Assertion :** If x = 2k – 1 and y = k is a solution of the equation 3x – 5y – 7 = 0, then the value of k is 10.**Reason:** A linear equation in two variables has infinitely many solutions

## Answer

Answer: (b)**Q.4. Assertion: **x + y = 3 is the equation of a line passing through the origin.**Reason:** y = 2x is the equation of a line passing through the origin.

## Answer

Answer: (d)**Q.5. Assertion:** X = 3 and y = 2 is a solution of the linear equation 2x + 3y = 12.**Reason:** X = 4 and y = 2 is a solution of the linear equation x + 3y = 10.

## Answer

Answer: (b)**Q.6. Assertion : **The point (3, 0) lies on the graph of the linear equation 4x + 3y = 12.**Reason:** (3, 0) satisfies the equation 4x + 3y = 12.

## Answer

Answer: (a)**Q.7. Assertion : **A linear equation 3x + 5y = 2 has a unique solution.**Reason: **A linear equation in two variables has infinitely many solutions.

## Answer

Answer: (d)We know that a linear equation in two variables has infinitely many solutions.

So, Reason is correct.

Hence, Assertion is not correct

Correct option is (d) Assertion (A) is false but reason (R) is true.

**Q.8. Assertion : **The graph of the linear equation 2x – y = 1 passes through the point (2, 3).**Reason:** Every point lying on graph is not a solution of 2x – y = 1.

## Answer

Answer: (c)**Q.9. Assertion: **y = 3x represents a line passing through the origin.**Reason:** Any line parallel to the x-axis is y = a.

## Answer

Answer: (b)**Q.10. Assertion : **The point (2, 2) is the solution of x + y = 4.**Reason: **Every point which satisfy the linear equation is a solution of the equation

## Answer

Answer: (a)**Q.11. Assertion: **X = 2 is a line parallel to the y-axis.**Reason:** The equation of a line parallel to the y-axis is x = a.

## Answer

Answer: (a)**Frequently Asked Questions (FAQs)**

**What is linear equation in two variables?**

An equation is said to be linear equation in two variables if it is written in the form of ax + by + c=0, where a, b and c are real numbers. The coefficients of x and y should not be zero.

For example, 5x+y = 4 and -x+2y = 5 are linear equations in two variables.

**What are the coefficients of x and y in the 5x-4y=6?**

Coefficient of x = 5, coefficient of y = -4

**What is the constant term of the equation 9x+2y=11**

11