NCERT Class 10 Maths — Chapter 3

Exercise 3.2: Graphical Method of Solving Linear Equations

Solve pairs of linear equations by drawing their graphs and reading the intersection point. Also convert word problems into equations first.

graphical solutionunique solution from graphword problems to equations

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Extra Practice Questions

These questions cover the same concepts as Exercise 3.2. Try solving them to build confidence before or after the textbook exercise.

For a pair of linear equations in two variables, (x, y) = (p, q) is a solution if:

A.It satisfies the first equation only.

B.It satisfies the second equation only.

C.It satisfies both equations simultaneously.

D.It is a point on the x-axis.

Ravi was solving the pair of linear equations x + 2y = 5 and 2x + 4y = 10 using the substitution method. His first step was to express x from the first equation as x = 5 - 2y. Then he substituted this into the second equation: 2(5 - 2y) + 4y = 10. What conclusion should Ravi draw after simplifying this equation?

A.There is a unique solution (x, y).

B.There is no solution to the system.

C.There are infinitely many solutions to the system.

D.Ravi made a mistake in the first step.

Consider the pair of linear equations: L1: (k+1)x + 8y = 4k and L2: kx + (k+3)y = 3k-1. If these lines are parallel, which of the following statements must be true?

A.k = -3

B.k = 1

C.k = 3

D.k = -1

Solve the following pair of linear equations for x and y: (a-b)x + (a+b)y = a² - 2ab - b² (a+b)x + (a+b)y = a² + b²

A.x = b, y = -a

B.x = a-b, y = (a² + b²)/(a+b)

C.x = a, y = -b

D.x = a+b, y = (a² - 2ab - b²)/(a+b)

For what values of p and q will the following pair of linear equations have infinitely many solutions? 2x + 3y = 7 (p+q)x + (2p-q)y = 21

A.p=5, q=1

B.p=3, q=1

C.p=4, q=2

D.p=5, q=2

Ravi was solving the pair of linear equations: Equation (1): x + 2y = 7 Equation (2): 3x + y = 11 He decided to use the substitution method. From Equation (1), he wrote x = 7 - 2y. Then he substituted this into Equation (2) as follows: 3(7 - 2y) + y = 11 21 - 6y + y = 11 21 - 7y = 11 Which of the following statements correctly identifies the mistake in Ravi's working (if any)?

A.There is no mistake in Ravi's working.

B.The mistake is in substituting x into Equation (2); he should have substituted into Equation (1) instead.

C.The mistake is in the algebraic simplification: -6y + y should be -5y, not -7y.

D.The mistake is that he should have expressed y in terms of x from Equation (1) instead of x in terms of y.

A two-digit number is such that the sum of its digits is 9. If 27 is added to the number, its digits are reversed. Let the number be 10x + y, where x is the tens digit and y is the units digit. Which pair of linear equations correctly represents this problem?

A.x + y = 9 and 10y + x - (10x + y) = 27

B.x + y = 9 and (10x + y) + 27 = 10y + x

C.x + y = 9 and (10y + x) + 27 = 10x + y

D.x - y = 9 and (10x + y) + 27 = 10y + x

The cost of 5 pens and 7 notebooks is ₹255, while the cost of 7 pens and 5 notebooks is ₹249. What is the cost of one pen and one notebook, respectively?

A.₹20, ₹25

B.₹22, ₹21

C.₹25, ₹20

D.₹21, ₹22

For what value of 'k' will the following pair of linear equations have no solution? 2x + 3y = 7 (k - 1)x + (k + 2)y = 3k

A.k = -7

B.k = 7

C.k = 3

D.k = -3

For what value of 'p' will the following pair of linear equations have no solution? (p+1)x - 3y = p-2 (p-2)x - (p+1)y = p

A.p = 1

B.p = 2