CBSE Class 9 Mathematics Linear Equations in two variables Assignment Set A

ASSERTION & REASONING QUESTIONS

DIRECTION : 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.

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

Question. 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.
(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.
Answer : We know that equation of a line parallel to the y-axis is x = a.
So, Reason (R) is true.
Also, x = 2 is a line parallel to the y-axis.
So, Assertion (A) is true.
Thus, Reason (R) and Assertion (A) are true and Reason (R) is a correct explanation of Assertion (A) .
Correct option is (a) Both assertion (A) and reason (R) are true and reason
(R) is the correct explanation of assertion (A) .

Question. 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 : For Assertion: The given linear equation is 2x + 3y = 12
Substituting x = 3 and y = 2, we get
LHS = 2 x 3 + 3 x 2 = 6 + 6 = 12 = RHS
So, Assertion is correct.
For Reason: The given linear equation is x + 3y = 10
Substituting x = 4 and y = 2, we get
LHS = 4 + 3 x 2 = 4 + 6 = 10 = RHS
So, Reason is also correct.
But reason (R) is not the correct explanation of assertion (A) .
Correct option is (b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A) .

Question. 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.
(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.
Answer : For Assertion: The given linear equation is x + y = 3
Since x = 0 and y = 0 is not satisfying x + y = 3, therefore it is not passing through the origin.
So, Assertion is not correct.
Since x = 0 and y = 0 is not satisfying y = 2x, therefore it is passing through the origin.
So, Reason is correct.
Correct option is (d) Assertion (A) is false but reason (R) is true.

Question. 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
(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.
Answer : 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 x 2 + 3 x 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) ..

Question. Assertion : There are infinite number of lines which passes through (3, 2) .
Reason : A linear equation in two variables has infinitely many solutions.
(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.
Answer : 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) Both assertion (A) and reason (R) are true and reason
(R) is not the correct explanation of assertion (A) .

Question. Assertion: y = 3x represents a line passing through the origin.
Reason: Any line parallel to the x-axis is y = a.
(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.
Answer : Since x = 0 and y = 0 is not satisfying y = 3x, therefore it is passing through the origin.
So, Assertion (A) is true.
Also, we know that equation of a line parallel to the x-axis is y = a.
So, Reason (R) is also true.
But Reason is not the correct explanation of Assertion.
Correct option is (b) Both assertion (A) and reason (R) are true and reason
(R) is not the correct explanation of assertion (A) .

Question. 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.
(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.
Answer : We know that a linear equation in two variables has infinitely many solutions. So, Reason is correct.
Since x = 2k - 1 and y = k is solution of the given linear equation, we have
3 x (2k – 1) – 5k – 7 = 0 ⇒ 6k – 3 – 5k – 7 = 0 ⇒ k – 10 = 0 ⇒ k = 10.
So, Assertion is also correct
But reason (R) is not the correct explanation of assertion (A) .
Correct option is (b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A) .

Question. 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 : For Assertion: The given linear equation is 2x + 3y = 12
Substituting x = 3 and y = 2, we get
LHS = 2 x 3 + 3 x 2 = 6 + 6 = 12 = RHS
So, Assertion is correct.
For Reason: The given linear equation is x + 3y = 10
Substituting x = 4 and y = 2, we get
LHS = 4 + 3 x 2 = 4 + 6 = 10 = RHS
So, Reason is also correct.
But reason (R) is not the correct explanation of assertion (A) .
Correct option is (b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A) .

Question. 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 : We know every point which satisfy the linear equation is a solution of the equation.
So, Reason (R) is true.
Substituting x = 2 and y = 2, we get
LHS = 2 + 2 = 4 = RHS
Since (3, 0) satisfies the equation 4x + 3y = 12, therefore the point (2, 2) is the solution of x + y = 4
So, Assertion (A) is also true.
Here, Reason is the correct explanation of Assertion.
Correct option is (a) Both assertion (A) and reason (R) are true and reason
(R) is the correct explanation of assertion (A) .

Question. 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.
(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.
Answer : For Assertion: The given linear equation is 2x – y = 1
Substituting x = 2 and y = 3, we get
LHS = 2 x 2 – 3 = 4 – 3 = 1 = RHS
Since (3, 0) satisfies the equation 4x + 3y = 12, therefore graph of the
linear equation 2x – y = 1 passes through the point (2, 3) .
So, Assertion is correct.
But Reason is not correct as every point lying on graph is a solution of
2x – y = 1.
Correct option is (c) Assertion (A) is true but reason (R) is false.

Please click the link below to download CBSE Class 9 Mathematics Linear Equations in two variables Assignment Set A