Class 10 / Maths

Class 10 Maths Pair of Linear Equations Worksheet

Practice substitution, elimination, consistency, and word problems for pairs of linear equations.

advanced45 minutesAnswer key included

Learning objective

Practise substitution, elimination, consistency checks, cross multiplication, and forming equations from word problems.

Questions

  1. Solve by substitution: x + y = 9 and x - y = 3.
  2. Solve by elimination: 2x + 3y = 13 and 3x - y = 5.
  3. Solve: 5x - 2y = 4 and 7x + 3y = 24.
  4. Determine whether 2x + 3y = 5 and 4x + 6y = 10 are consistent.
  5. Determine whether x - 2y = 3 and 2x - 4y = 8 are consistent.
  6. The sum of two numbers is 50 and their difference is 14. Find the numbers.
  7. A two-digit number has sum of digits 9. If 27 is added to the number, the digits reverse. Find the number.
  8. Five pencils and three pens cost Rs. 65. Three pencils and two pens cost Rs. 40. Find the cost of each.
  9. Solve using cross multiplication: 2x + 3y = 8 and 3x + 2y = 7.
  10. Find k if kx + 3y = 7 and 2x + 6y = 14 have infinitely many solutions.

Answer key

Show suggested answers
  1. Adding the equations gives 2x = 12, so x = 6. Then y = 3.
  2. From 3x - y = 5, y = 3x - 5. Substitute in 2x + 3y = 13: 2x + 9x - 15 = 13, so x = 28/11 and y = 29/11.
  3. Multiply the first equation by 3 and the second by 2: 15x - 6y = 12 and 14x + 6y = 48. Add to get 29x = 60, so x = 60/29 and y = 92/29.
  4. The second equation is twice the first, so the pair is consistent with infinitely many solutions.
  5. For x - 2y = 3 and 2x - 4y = 8, the left side ratio is same but constants do not match, so the pair is inconsistent.
  6. Let the numbers be x and y. x + y = 50 and x - y = 14. Solving gives x = 32 and y = 18.
  7. Let tens digit be x and units digit be y. x + y = 9 and 10x + y + 27 = 10y + x. This gives x = 3, y = 6, so the number is 36.
  8. Let pencil cost be x and pen cost be y. 5x + 3y = 65 and 3x + 2y = 40. Solving gives x = 10 and y = 5.
  9. Solving 2x + 3y = 8 and 3x + 2y = 7 gives x = 1 and y = 2.
  10. For infinitely many solutions, k/2 = 3/6 = 7/14. Since both ratios equal 1/2, k = 1.

How to use this worksheet

Students can solve the questions independently first, then review errors with a parent or teacher. Teachers can use it as a short class activity, homework sheet, or revision check.

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