NCERT Class 10 Maths — Chapter 3

Exercise 3.4: Elimination Method

Multiply equations to make one variable's coefficients equal, then add or subtract to eliminate it. The most commonly used method in exams.

elimination methodequating coefficientsadding or subtracting equations

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Extra Practice Questions

These questions cover the same concepts as Exercise 3.4. Try solving them to build confidence before or after the textbook exercise.

A part of monthly hostel charges is fixed and the remaining depends on the number of days one has taken food in the mess. When a student A takes food for 20 days, she has to pay ₹1000 as hostel charges, whereas a student B, who takes food for 26 days, pays ₹1180 as hostel charges. Find the fixed charges and the cost of food per day.

A.Fixed charges = ₹100, Cost per day = ₹30

B.Fixed charges = ₹150, Cost per day = ₹40

C.Fixed charges = ₹400, Cost per day = ₹30

D.Fixed charges = ₹300, Cost per day = ₹35

A fraction becomes 9/11 if 2 is added to both the numerator and the denominator. If 3 is added to both the numerator and the denominator, it becomes 5/6. What is the fraction?

A.7/9

B.5/7

C.7/11

D.3/5

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%

For what value of k will the system of equations kx + 3y = k-3 and 12x + ky = k have no solution?

A.k=6

B.k=-6

C.k=0

D.k=9

Solve the following pair of equations: 2/x + 3/y = 13 5/x - 4/y = -2

A.x = 1/2, y = 1/3

B.x = 2, y = 3

C.x = 1/2, y = -1/3

D.x = -2, y = -3

Ravi was asked to find the value of 'k' for which the system of equations kx + 2y = 5 and 3x + y = 1 has a unique solution. He stated k = 6. What was his mistake?

A.He used the condition for no solution.

B.He used the condition for infinitely many solutions.

C.He incorrectly solved the inequality for 'k'.

D.He misunderstood the concept of a unique solution.

For what value of 'k' will the pair of linear equations x + ky = 3 and 3x + 2y = 1 NOT have a unique solution?

A.2/3

B.1/3

C.-2/3

D.-1/3

For the pair of linear equations: ax + by + c = 0 dx + ey + f = 0 Which of the following statements correctly represents the setup for finding 'x' using the cross-multiplication method?

A.x / (bf - ce) = 1 / (ae - bd)

B.x / (be - cf) = 1 / (af - cd)

C.x / (bf - ce) = y / (cd - af)

D.x / (ae - bd) = 1 / (bf - ce)

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

Which of the following statements is FALSE regarding a pair of linear equations a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0, if a1/a2 = b1/b2 = c1/c2?

A.The lines representing the equations are coincident.

B.The system has infinitely many solutions.

C.The system is consistent.

D.The lines representing the equations are parallel and distinct.

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