NCERT Class 10 Maths — Chapter 3

Exercise 3.1: Graphical Representation of Linear Equations

Plot pairs of linear equations on a graph and see whether they intersect (one solution), overlap (infinite solutions), or run parallel (no solution).

graphing linear equationsconsistent and inconsistent systemsparallel lines

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These questions cover the same concepts as Exercise 3.1. Try solving them to build confidence before or after the textbook exercise.

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

Solve the following pair of linear equations using the substitution method: x + y = 14 x - y = 4

A.x = 9, y = 5

B.x = 5, y = 9

C.x = 7, y = 7

D.x = 10, y = 4

A two-digit number is such that the product of its digits is 14. If 45 is added to the number, the digits interchange their places. What is the sum of the digits of the original number?

A.6

B.7

C.8

D.9

Solve for x and y: (a-b)x + (a+b)y = 2a (a+b)x + (a-b)y = 2b

A.x = 1, y = 1

B.x = (a+b)/(a²+b²), y = (a-b)/(a²+b²)

C.x = (a+b)/(a²-b²), y = (a-b)/(a²-b²)

D.x = (a²+b²)/(a-b), y = (a²+b²)/(a+b)

If x and y are two numbers such that their sum is 8 and twice the first number minus the second number is 7, which pair of linear equations represents this?

A.x + y = 7, 2x - y = 8

B.x + y = 8, x - 2y = 7

C.x + y = 8, 2x + y = 7

D.x + y = 8, 2x - y = 7

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.

A pair of linear equations that has no solution is called an _______ system.

A.consistent

B.dependent

C.independent

D.inconsistent

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.

Consider the pair of equations: Equation (1): x - 2y = 4 Equation (2): 3x + y = 5 Which method would be the most efficient to solve this particular system of equations and why?

A.Substitution method, because 'y' in Equation (2) can be easily isolated.

B.Elimination method, because the coefficients of 'x' are already multiples of each other.

C.Cross-multiplication method, because it is always the fastest method for any system.

D.Graphical method, because it always gives the exact solution quickly.

A chemist has two solutions of hydrochloric acid in water. One solution contains 20% acid and the other contains 60% acid. How many milliliters of each solution should be mixed to obtain 100 ml of a solution containing 40% acid?

A.40 ml of 20%, 60 ml of 60%

B.50 ml of 20%, 50 ml of 60%

C.60 ml of 20%, 40 ml of 60%

D.75 ml of 20%, 25 ml of 60%

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