SSC Linear Equations in Two Variables Questions with Answers

Linear equations in two variables are a regular part of the SSC algebra and word problem section. This practice paper has 15 questions on simultaneous equations, ages, numbers and fractions with solutions.

Practice Paper at a Glance

Linear Equations in Two Variables: Concept in Simple Words

An equation of the form ax + by + c = 0 is linear in two variables. A pair of such equations can have one solution, no solution or infinitely many solutions depending on the ratios of the coefficients. You can solve a pair by substitution, elimination or cross multiplication.

Types of Solutions

Tips and Shortcuts for SSC Linear Equations in Two Variables

• Add and subtract the equations when the coefficients are swapped, such as 5x + 3y and 3x + 5y.
• Test the options when only the value of one variable is asked.
• For "find k" questions use the ratio conditions.
• Write the meaning of x and y before forming equations in word problems.

Set 1: Solving Pairs of Equations (Q1–Q8)

Q1. Solve x + y = 10 and x − y = 2. Find x.
Answer: 6
Solution: Adding gives 2x = 12, so x = 6 and y = 4.

Q2. Solve 2x + 3y = 13 and 3x − y = 3. Find x.
Answer: 2
Solution: From the second, y = 3x − 3. Then 2x + 9x − 9 = 13, so x = 2.

Q3. The sum of two numbers is 45 and their difference is 9. Find the larger number.
Answer: 27
Solution: (45 + 9) / 2 = 27.

Q4. For what value of k do kx + 3y = 5 and 2x + 6y = 10 have infinitely many solutions?
Answer: 1
Solution: k/2 = 3/6 = 5/10 = 1/2, so k = 1.

Q5. For what value of k do 3x + ky = 9 and x + 2y = 5 have no solution?
Answer: 6
Solution: 3/1 = k/2, so k = 6 (and 9/5 is different).

Q6. Solve 5x + 3y = 21 and 3x + 5y = 19. Find x.
Answer: 3
Solution: Adding: x + y = 5. Subtracting: x − y = 1. So x = 3.

Q7. Solve 3x − 2y = 1 and x + y = 7. Find x.
Answer: 3
Solution: y = 7 − x, so 3x − 14 + 2x = 1, x = 3 and y = 4.

Q8. Solve 2x + y = 7 and x − y = 2. Find y.
Answer: 1
Solution: Adding: 3x = 9, so x = 3 and y = 1.

Set 2: Word Problems (Q9–Q15)

Q9. A father is 3 times as old as his son. After 12 years he will be twice as old. Find the son's age.
Answer: 12 years
Solution: 3s + 12 = 2(s + 12), so s = 12.

Q10. 5 pens and 3 pencils cost ₹47. 3 pens and 5 pencils cost ₹41. Find the price of one pen.
Answer: ₹7
Solution: Adding gives 8(p + q) = 88, subtracting gives p − q = 3, so p = 7.

Q11. A fraction becomes 1 if 1 is added to the numerator and 1/2 if 1 is added to the denominator. Find the fraction.
Answer: 2/3
Solution: x + 1 = y and 2x = y + 1, so x = 2, y = 3.

Q12. The sum of the digits of a two-digit number is 9. The number obtained by reversing the digits is 27 more. Find the number.
Answer: 36
Solution: y − x = 3 and x + y = 9, so x = 3, y = 6.

Q13. A is 8 years older than B and the sum of their ages is 40. Find A's age.
Answer: 24 years
Solution: A = (40 + 8) / 2 = 24.

Q14. A boat goes 30 km downstream in 3 hours and 18 km upstream in 3 hours. Find the speed of the boat in still water.
Answer: 8 km/h
Solution: Downstream 10, upstream 6, so the boat = (10 + 6) / 2 = 8.

Q15. The perimeter of a rectangle is 28 cm and its length is 2 cm more than its breadth. Find the length.
Answer: 8 cm
Solution: l + b = 14 and l − b = 2, so l = 8.

Common Mistakes in Linear Equations in Two Variables

• Not checking the answer in both equations.
• Making sign errors while subtracting equations.
• Using the wrong meaning for x and y in word problems.
• Forgetting that the ratio conditions are for the coefficients only.

How to Practise These 15 Questions

1. Read the concept and tips once.
2. Attempt Set 1 without looking at the answers.
3. Check the answers and read the solution for every wrong question.
4. Repeat the paper after three days to see the improvement.

Related Topics to Study Next

• Quadratic Equations Questions
• Problems on Ages Questions
• Algebra Questions
• Quantitative Aptitude Notes
• All SSC Practice Papers
• SSC Previous Year Papers

Frequently Asked Questions

What is a linear equation in two variables?

An equation of the form ax + by + c = 0 whose graph is a straight line.

How many solutions can a pair of linear equations have?

One, none or infinitely many.

Which method is fastest in SSC?

Elimination, or testing the options when they are given.

How do I find k for infinite solutions?

Equate a1/a2 = b1/b2 = c1/c2 and solve for k.

How many questions are there in this practice paper?

This paper has 15 questions in 2 sets, each with the answer and a short solution.

Is this practice paper useful for SSC CGL, CHSL and MTS?

Yes. The questions follow the level asked in SSC CGL, CHSL, MTS, GD and CPO exams, and are also useful for other government exams.

How much time should I take to solve this paper?

Try to finish the 15 questions in about 15 to 20 minutes, then check the answers and revise the mistakes.

How should I use this practice paper for best results?

First read the concept and tips, then attempt each set without looking at the answers, and note the questions you got wrong for revision.

Where can I find more practice papers like this?

You can find more topic-wise practice papers on the SSC Education practice paper page, and previous year papers on the PYQ page.

Are the notes for this topic available?

Yes. Read the Quantitative Aptitude notes on SSC Education for detailed theory before attempting the questions.