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PracticeClass 10Chapter 03: Pair of Linear Equations in Two Variables
CLASS 10 · CHAPTER 03

Pair of Linear Equations in Two Variables
Practice Questions

20 curated NCERT & Board Exam questions to test your understanding. Click on "Show Solution & Answer" to check step-by-step working.

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Q1MCQ1 Mark

The pair of equations x + 2y + 5 = 0 and -3x - 6y + 1 = 0 has:

Q2MCQ1 Mark

If a pair of linear equations is consistent, then the lines will be:

Q3MCQ1 Mark

Value of k for which 3x - y + 8 = 0 and 6x - ky + 16 = 0 represent coincident lines is:

Q4MCQ1 Mark

The solution of equations x + y = 7 and 2x - 3y = 9 is:

Q5Assertion-Reason1 Mark

Assertion (A): System of equations 2x + 3y = 7 and 4x + 6y = 14 has infinitely many solutions. Reason (R): If a₁/a₂ = b₁/b₂ = c₁/c₂, system of equations is dependent and consistent.

Q6Assertion-Reason1 Mark

Assertion (A): Lines x = 2 and y = 3 intersect at point (2, 3). Reason (R): Line x = a is parallel to y-axis and y = b is parallel to x-axis.

Q7Short Answer2 Marks

Solve for x and y: x + y = 14, x - y = 4.

Q8Short Answer2 Marks

Solve by elimination: 2x + 3y = 11 and 2x - 4y = -24.

Q9Short Answer2 Marks

Find condition for unique solution of 4x + py + 8 = 0 and 2x + 2y + 2 = 0.

Q10Short Answer2 Marks

Find k if kx + 3y = k - 3 and 12x + ky = k have infinitely many solutions.

Q11Short Answer2 Marks

Sum of digits of two-digit number is 9. 9 times number is twice reversed number. Find number.

Q12Long Answer3 Marks

Solve graphically: 2x + 3y = 12 and x - y = 1. Find y-axis triangle vertices.

Q13Long Answer3 Marks

Fraction becomes 9/11 if 2 added to num & den, 5/6 if 3 added. Find fraction.

Q14Long Answer3 Marks

Five years ago Nuri was thrice as old as Sonu. Ten years later Nuri will be twice as old. Find ages.

Q15Long Answer3 Marks

Meena withdrew ₹2000 in ₹50 and ₹100 notes (total 25 notes). Find count of each note.

Q16Case Study4 Marks

Case Study Scenario: A test has 1-mark and 2-mark questions. Total questions = 40, total marks = 60. Question: Find number of 1-mark and 2-mark questions.

Q17Case Study4 Marks

Case Study Scenario: A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours it goes 40 km upstream & 55 km downstream. Question: Find speed of boat in still water and speed of stream.

Q18PYQ5 Marks

2 women & 5 men finish work in 4 days, 3 women & 6 men in 3 days. Find time for 1 woman alone.

Q19PYQ5 Marks

If 217x + 131y = 913 and 131x + 217y = 827, find x + y.

Q20PYQ5 Marks

Solve for x and y: ax + by = a - b, bx - ay = a + b.