Two Variables, One Line — Class 9 MCQs with Answers
Class 9 CBSE Mathematics · Chapter 13
90 practice questions · 30 Easy · 30 Medium · 30 Hard · Updated
Practise the most important Class 9 CBSE Mathematics questions from Chapter 13, "Two Variables, One Line". You get 9 timed quizzes made from 90 NCERT-based MCQs, with answers and explanations. The questions are split into 30 Easy, 30 Medium and 30 Hard. Warm up on the basics, then move on to the exam-level questions that top scorers in CBSE Board exams and the JEE & NEET foundation years get right.
To score well in "Two Variables, One Line", focus on fast problem-solving, formula recall and step-by-step working. Each MCQ here is timed and uses exam-style marking (+4 correct, −1 wrong, 0 skipped). This helps you stay accurate when time is short, just as real papers need. Every question has a short explanation, so a wrong answer becomes a quick lesson. It is the fastest way to fix gaps before a test.
Use this chapter for focused revision. Start with the Easy set to check your basics on Two Variables, One Line, then move to Medium and Hard to practise applying them. Your accuracy, streaks and XP save automatically. This chapter also adds to your overall Class 9 Mathematics mastery score. 14 sample questions are solved in full below, with the answer and a worked explanation. Sign in free to start practising.
Two Variables, One Line — important questions & MCQs with answers (Class 9 Mathematics)
14 solved questions from this chapter's difficulty levels, each with its answer and explanation.
- Q1Easy
Which of these is a linear equation in two variables?
A.x² + y = 4B.3x + 5y = 11✓ CorrectC.xy = 6D.2/x + y = 1Answer: B. 3x + 5y = 11
Explanation: 3x + 5y = 11 has the form ax + by + c = 0 with both variables to the power 1. The others have x², a product xy, or x in the denominator, so they are not linear.
- Q2Easy
Which ordered pair is a solution of 2x + 5y = 20?
A.(2, 5)B.(4, 3)C.(0, 5)D.(5, 2)✓ CorrectAnswer: D. (5, 2)
Explanation: For (5, 2): 2 × 5 + 5 × 2 = 20, so it works. The pair (2, 5) gives 4 + 25 = 29; the order matters, because the first number is always x.
- Q3Easy
What is the slope of the line through (1, 2) and (5, 10)?
A.1/2B.8C.2✓ CorrectD.3Answer: C. 2
Explanation: Slope = rise/run = (10 − 2)/(5 − 1) = 8/4 = 2. Run over rise gives 1/2, which is upside down.
- Q4Easy
The sum of two numbers x and y is 31 and their difference (x minus y) is 9. Which pair of equations shows this?
A.x + y = 9 and x − y = 31B.x + y = 31 and xy = 9C.x + y = 31 and x = 9yD.x + y = 31 and x − y = 9✓ CorrectAnswer: D. x + y = 31 and x − y = 9
Explanation: Sum 31 gives x + y = 31 and difference 9 gives x − y = 9. Swapping 31 and 9, or using a product xy, describes a different puzzle.
- Q5Easy
Solve x + y = 40 and x − y = 14.
A.x = 27, y = 13✓ CorrectB.x = 13, y = 27C.x = 26, y = 14D.x = 17, y = 23Answer: A. x = 27, y = 13
Explanation: Adding gives 2x = 54, so x = 27, and then y = 40 − 27 = 13. The order matters: x − y = 14 needs x to be the larger number.
- Q6Easy
When the graphs of two linear equations are parallel lines, how many solutions does the pair have?
A.Infinitely manyB.Exactly oneC.Exactly twoD.No solution✓ CorrectAnswer: D. No solution
Explanation: Parallel lines never meet, so no point lies on both lines and the pair has no solution.
- Q7Medium
Write 0.5x − 3 = (2/3)y in standard form with integer coefficients.
A.3x + 4y − 18 = 0B.3x − 4y − 3 = 0C.3x − 4y − 18 = 0✓ CorrectD.3x − 4y + 18 = 0Answer: C. 3x − 4y − 18 = 0
Explanation: First move all terms left: 0.5x − (2/3)y − 3 = 0. Multiply by 6 to get 3x − 4y − 18 = 0; the constant −3 must also be multiplied by 6.
- Q8Medium
(2, −1) is a solution of both 2mx + 3y = 9 and 4x + ny = 2. Find m and n.
A.m = 3/2, n = 6B.m = 3, n = −6C.m = 3, n = 6✓ CorrectD.m = 6, n = 6Answer: C. m = 3, n = 6
Explanation: First: 2m(2) + 3(−1) = 9 gives 4m = 12, so m = 3. Second: 4(2) + n(−1) = 2 gives −n = −6, so n = 6. Using y = +1 instead of −1 gives the wrong m = 3/2.
- Q9Medium
Find the slope of the line through A(−3, 4) and B(1, −4).
A.−2✓ CorrectB.2C.−1/2D.−8Answer: A. −2
Explanation: Rise = −4 − 4 = −8 and run = 1 − (−3) = 4, so slope = −8/4 = −2. The line falls from left to right, so the slope must be negative.
- Q10Medium
A taxi has a fixed charge ₹x and a charge of ₹y per km. A 5 km ride costs ₹110 and a 9 km ride costs ₹170. Which pair of equations fits?
A.5x + y = 110 and 9x + y = 170B.x + y = 110 and x + y = 170C.x + 5y = 110 and x + 9y = 170✓ CorrectD.5x + 9y = 280 and x + y = 60Answer: C. x + 5y = 110 and x + 9y = 170
Explanation: The fixed charge is paid once and the per-km charge is multiplied by the distance, so x + 5y = 110 and x + 9y = 170. Multiplying the fixed charge by the km is the usual slip.
- Q11Medium
Solve x + 3y = 7 and 2x − y = 0 by substitution.
A.x = 2, y = 1B.x = 1, y = 2✓ CorrectC.x = 7, y = 0D.x = 0, y = 0Answer: B. x = 1, y = 2
Explanation: From the second equation y = 2x. Then x + 6x = 7, so x = 1 and y = 2. (7, 0) fits only the first equation and (0, 0) only the second.
- Q12Hard
For which value of k is (k − 2)x + (k² − 4)y + 5 = 0 NOT a linear equation in two variables?
A.k = −2B.k = 2 or k = −2C.No value of kD.k = 2✓ CorrectAnswer: D. k = 2
Explanation: The equation stops being linear in two variables only when a and b are both zero. k − 2 = 0 and k² − 4 = 0 together need k = 2; at k = −2, a = −4 ≠ 0, so it is still linear.
- Q13Hard
(p, p + 1) is a solution of 3x − 2y = 4, and (q, 2q) is a solution of x + y = 9. Find p + q.
A.5B.10.5C.6D.9✓ CorrectAnswer: D. 9
Explanation: 3p − 2(p + 1) = 4 gives p − 2 = 4, so p = 6. q + 2q = 9 gives q = 3. So p + q = 9; writing −2(p + 1) as −2p + 2 gives the wrong p = 2.
- Q14Hard
The points A(1, 2), B(3, 8) and C(k, 14) lie on one line. Find k.
A.37B.5✓ CorrectC.7D.9Answer: B. 5
Explanation: Slope AB = (8 − 2)/(3 − 1) = 3. The slope from A to C must also be 3: (14 − 2)/(k − 1) = 3, so k − 1 = 4 and k = 5. Using run/rise instead gives k = 37.
Key concepts: Two Variables, One Line (Class 9 Mathematics)
A linear equation in two variables has infinitely many solutions that form one straight line. The chapter covers standard form, slope and y-intercept in y = mx + d, and solving a pair of equations by substitution, elimination or graphs, with ratio tests for one, none or infinitely many solutions.
- Linear equation in two variables
- Any equation that can be written as ax + by + c = 0, where a, b, c are real numbers and a and b are not both zero. Radha's fruit bill 60x + 50y = 280 is an example.
- Standard form
- ax + by + c = 0, with a and b the coefficients of x and y and c the constant. Clear fractions by multiplying every term, including c, by the same number; ax + c = 0 is the special case b = 0.
- Solution as an ordered pair
- A pair (x, y) that makes the equation true, such as (2, 3) for 3x + 2y = 12. Order matters: the first number is always x, so (3, 2) is a different point.
- Infinitely many solutions
- Pick any value u for x, solve the one-variable equation left for y, and you get a solution (u, v). So one linear equation in two variables never has just one solution.
- Graph of a linear equation
- All solutions lie on one straight line, and every point on that line is a solution. Putting x = 0 and then y = 0 quickly gives the points where the line cuts the y-axis and the x-axis.
- Lines through the origin
- If c = 0, then (0, 0) satisfies ax + by = 0, so the line passes through the origin whatever a and b are; and a line through the origin must have c = 0. x = 0 is the y-axis and y = 0 is the x-axis.
- Slope (gradient) as rise over run
- Slope = rise/run = (y₂ − y₁)/(x₂ − x₁) for any two points on the line. It is the same whichever two points you pick and whichever order you take them in.
- Slope-intercept form y = mx + d
- m is the slope and d is the y-intercept, so the line cuts the y-axis at (0, d). From ax + by + c = 0 with b ≠ 0, m = −a/b and d = −c/b.
- Sign of the slope
- A positive slope goes up from left to right, a negative slope goes down, and a horizontal line such as y = 5 has slope 0. A vertical line such as x = 2 has run 0, so its slope is undefined.
- Pair of linear equations
- Two equations a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 in the same two variables, built from word problems like Rakesh's puzzle or ticket prices. A solution must satisfy both equations at once.
- Substitution method
- Write one variable in terms of the other from one equation, put it into the other equation, and solve the one-variable equation that is left. Then substitute back to find the second variable.
- Elimination method
- Multiply the equations so one variable has the same coefficient in both, then add or subtract to remove it. This is the same idea as the fangcheng method in China's Nine Chapters, also used by Āryabhaṭa and Brahmagupta.
- Ratio tests for the nature of solutions
- a₁/a₂ ≠ b₁/b₂ gives a unique solution; a₁/a₂ = b₁/b₂ = c₁/c₂ gives infinitely many; a₁/a₂ = b₁/b₂ ≠ c₁/c₂ gives none. In elimination, ending with 0 = 0 means infinitely many and 0 = a non-zero number means none.
- Graphical method
- Draw both lines: intersecting lines give one solution (the meeting point), coincident lines give infinitely many, and parallel lines (same slope, different intercepts) give no solution.
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Start this chapter free →Two Variables, One Line — FAQs
What are the key concepts in Class 9 Mathematics Two Variables, One Line?+
A linear equation in two variables has infinitely many solutions that form one straight line. The chapter covers standard form, slope and y-intercept in y = mx + d, and solving a pair of equations by substitution, elimination or graphs, with ratio tests for one, none or infinitely many solutions. Key ideas include Linear equation in two variables, Standard form, Solution as an ordered pair, Infinitely many solutions, Graph of a linear equation, Lines through the origin.
What does Class 9 Mathematics Chapter 13 (Two Variables, One Line) cover on XamBaaz?+
It has 90 NCERT-based MCQs on "Two Variables, One Line": 30 Easy, 30 Medium and 30 Hard. Together they make 9 timed quizzes, and you never get the same set twice. Every question has an instant explanation. They help you prepare for CBSE Board exams and the JEE & NEET foundation years.
Are these "Two Variables, One Line" questions free to practise?+
Yes. Sign in with Google to practise "Two Variables, One Line" free. Full unlimited access is ₹999/year. One year from the day you pay. You stay in Class 9 till 31 March; on 1 April your account moves up to Class 10 and the rest of your year carries over. No chapter is charged separately.
How should I revise "Two Variables, One Line" for the exam?+
Start with the Easy quiz to check your basics, then try Medium and Hard to practise applying them. There are 9 timed quizzes on this chapter, so you can come back for a fresh set instead of one you have seen. Read each explanation, retry the questions you miss, and track your accuracy until it stays high.
Are these "Two Variables, One Line" MCQs available with answers?+
Yes. 14 sample questions are shown here in full, each with the correct option and a step-by-step "Why" explanation. Sign in free with Google to start practising, with instant scoring.
Is there negative marking in the "Two Variables, One Line" quizzes?+
Yes. The timed quizzes use exam-style marking: +4 for a right answer, −1 for a wrong one and 0 for a skip. MHT-CET and CBSE board papers have no negative marking. Our mocks for those are scored their way.
What are the important questions from Two Variables, One Line (Class 9 Mathematics)?+
The questions that matter most test Linear equation in two variables, Standard form, Solution as an ordered pair, Infinitely many solutions, Graph of a linear equation, Lines through the origin. This page shows 14 solved important MCQs with answers and explanations. Sign in to practise all 90 questions on the chapter as timed quizzes.
Is there an online quiz for Two Variables, One Line?+
Yes — Class 9 Mathematics Two Variables, One Line has timed online quizzes at Easy, Medium and Hard levels, with instant scoring and a worked explanation on every question. The first quiz on the chapter is free.