**Assertion and Reason Questions for Class 10 Maths Chapter 3 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:** The graph of the linear equations 3x+2y=12 and 5x-2y=4 gives a pair of intersecting lines. **Reason: **The graph of linear equations a_{1}x+b_{1}y+c_{1}=0 and a_{2}x+b_{2}y+c_{2}=0 gives a pair of intersecting lines if a_{1}/a_{2} ≠ b_{1}/b_{2}

## Answer

Answer: (a)**Q.2. Assertion:** If the pair of lines are coincident, then we say that pair of lines is consistent and it has a unique solution. **Reason:** If the pair of lines are parallel, then the pairs has no solution and is called inconsistent pair of equations.

## Answer

Answer: (d)**Q.3. Assertion: **The linear equations x-2y-3=0 and 3x+4y-20=0 have exactly one solution **Reason: **The linear equation 2x+3y-9=0 and 4x+6y-18=0 have a unique solution.

## Answer

Answer: (c)**Q.4. Assertion: **The graphical representation of the equations x+2y=3 and 2x+4y+7=0 gives a pair of coincident lines. **Reason: **The graph of linear equations a_{1}x+b_{1}y+c_{1}=0 and a_{2}x+b_{2}y+c_{2}=0 gives a pair of intersecting lines if a_{1}/a_{2} ≠ b_{1}/b_{2}

## Answer

Answer: (d)**Q.5. Assertion: **The value of k for which the system of equations 3x+ky=0 and 2x-y=0 has a unique solution is k ≠ -3/2 **Reason:** The graph of linear equations a_{1}x+b_{1}y+c_{1}=0 and a_{2}x+b_{2}y+c_{2}=0 gives a pair of intersecting lines if a_{1}/a_{2} ≠ b_{1}/b_{2}

## Answer

Answer: (a)**Q.6. Assertion: **The number of common solutions for the system of linear equations 5x+4y+6=0 and 10x+8y=12 is zero. **Reason: **The graph of linear equations a_{1}x+b_{1}y+c_{1}=0 and a_{2}x+b_{2}y+c_{2}=0 gives a pair of intersecting lines if a_{1}/a_{2} ≠ b_{1}/b_{2}

## Answer

Answer: (b)**Q.7. Assertion: **The value of k for which the system of linear equations 3x-4y=7 and 6x-8y=k have infinite number of solution is 14. **Reason: **The graph of linear equations a_{1}x+b_{1}y+c_{1}=0 and a_{2}x+b_{2}y+c_{2}=0 gives a pair of intersecting lines if a_{1}/a_{2} ≠ b_{1}/b_{2}

## Answer

Answer: (c)**Q.8. Assertion: **A pair of linear equations has no solution (s) if it is represented by intersecting lines graphically. **Reason: **If the pair of lines are intersecting, then the pair has unique solution and is called consistent pair of equations.

## Answer

Answer: (d)**Q.9. Assertion: **The value of q=±2, if x=3, y=1 is the solution of the line 2x+y-q^{2}-3=0. **Reason: **The solution of the line will satisfy the equation of the line.

## Answer

Answer: (a)**Q.10. Assertion: **The value of k for which the system of linear equations kx-y=2 and 6x-2y=3 has a unique solution is 3. **Reason: **The graph of linear equations a_{1}x+b_{1}y+c_{1}=0 and a_{2}x+b_{2}y+c_{2}=0 gives a pair of intersecting lines if a_{1}/a_{2} ≠ b_{1}/b_{2}