Class 10 Math: Pair of Linear Equations in Two Variables Important Exam Questions

NexPro Tools Mathematics TeamJune 5, 20266 min read

Preparing for school exams or final CBSE boards requires practicing questions patterned after official grading schemes. We have compiled a list of crucial questions for Class 10 Pair of Linear Equations in Two Variables to help you test your mastery.

Exam-Pattern Questions and Answers

Question 1 (EASY)

The pair of linear equations 2x = 5y + 6 and 15y = 6x - 18 represents two lines which are:
  • Option 1: intersecting
  • Option 2: parallel
  • Option 3: coincident
  • Option 4: either intersecting or parallel

Solution Explanation & Steps: (c) coincident Given equations can be rewrite as: 2x - 5y - 6 = 0 6x - 15y - 18 = 0 1 2 2 1 6 3 a a = = , 1 2 5 1 15 3 b b -= =- and 1 2 6 1 18 3 c c -= =- Therefore, the pair of equations has infinitely many solutions. Graphically pair of linear equations represent coincident.

Question 2 (EASY)

Assertion (A): If the co-ordinates of the mid-points of the sides AB and AC of ΔABC are D(3,5) and E(-3,-3) respectively, then BC = 20 units Reason (R): The line joining the mid points of two sides of a triangle is parallel to the third side and equal to half of it.
  • Option 1: Option A
  • Option 2: Option B
  • Option 3: Option C
  • Option 4: Option D

Solution Explanation & Steps: (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) For reason: By midpoint theorem, the line joining the mid points of two sides of a triangle is parallel to the third side and equal to half of it. So, reason is also true. SECTION - B Questions 21 to 25 carry 2 marks each.

Question 3 (MEDIUM)

Solve the following system of linear equations: 7x - 2y = 5 and 8x + 7y= 15 and verify your

This is a descriptive problem. Work out all steps on paper before checking the solution.

Solution Explanation & Steps: wer. Ans. Given system of linear equations: 7x - 2y = 5 ...(i) 8x + 7y = 15 ...(ii) Multiplying eq (i) by 7 and eq (ii) by 2 then adding, we get 65x = 65 ⇒ x = 1 Substituting value of x is eq (i) we get 7(1) - 2y = 5 ⇒ 7 - 2y = 5 ⇒ -2y = -2 or, y = 1 Therefore, x = 1 and y = 1

Grading Step-Marking Guidelines

Remember that teachers award partial marks for writing down formulas, stating the given variables, and drawing diagrams. Never leave a question blank on an exam. Write down the relevant formulas and initial substitution steps to secure partial credits.

📚 Class 10 Math Resource Hub for Pair of Linear Equations in Two Variables: • 🧮 Interactive Solver: Solve Pair of Linear Equations in Two Variables Problems - Verify steps in real-time. • 📝 Timed Practice Quiz: Take Pair of Linear Equations in Two Variables Online Quiz - Test your speed and concepts. • 📄 Printable Worksheet: Download Pair of Linear Equations in Two Variables PDF Worksheet - Interactive problems with answers. • 📐 Formula Sheet: View Pair of Linear Equations in Two Variables Key Equations - Complete revision references. • 🔄 Next Topic Guide: Quadratic Equations Study Notes • 🎓 Syllabus Overview: Class 10 Mathematics Portal - Access all chapter guides.