NCERT Class 10 Maths • Chapter 3
Pair of Linear Equations in Two Variables Class 10 Worksheet
Connect two equations with one common solution. Practise graphs, substitution, elimination and real-life modelling with this Pair of Linear Equations Class 10 worksheet.
Attempt the 20-question online quiz, then explore 10 interactive revision sets with five questions each. Each set progresses from easy practice to a more demanding reasoning task.
Pair of Linear Equations Online Quiz for Class 10
Question 1 of 20 • Core reasoning • Answered 0/20
If 7x + 5y = 31 and 3x − 5y = −1, find 2x − y.
Linear Equations Online Games for Class 10
Locate intersections, solve elimination challenges, repair substitution steps, build equations and organise mathematical arguments. Each game contains five questions.
1. Intersection Detective
Use the graph and equations together. The final challenge adds a third line through the intersection.
Locate the common point of the purple and green lines.
x + y = 5
2x − y = 4
Tap the graph to select integer coordinates, or type your answer below.
2. Elimination Workshop
Work with positive, negative and fractional solutions. Write your equation multipliers in your notebook.
Choose suitable multipliers and solve by elimination.
2x + y = 9
x − y = 3
3. Substitution Repair Lab
Repair the coefficient and constant after substitution. Finish by diagnosing an incorrect uniqueness claim.
Use x = 2 + y. Complete the substituted equation Ay + B = 13, then find x and y.
x − y = 2
2x + y = 13
4. Equation Forge
Construct missing coefficients from geometric conditions instead of solving only ready-made pairs.
Make both equations pass through (2, 5). Find the missing constants.
2x + y = p
−x + 3y = q
5. Build the Mathematical Argument
Tap the reasoning cards in order. Use Undo if you want to change the argument.
Arrange the four steps into a valid elimination argument.
x + y = 7
x − y = 3
Linear Equations HOTS Online Activities for Class 10
Investigate parameters, compare costs, interpret age timelines, decode digits and examine how changing data affects a solution. Use Next Question for more practice in the same skill.
6. Parameter Investigation
Use proportional equations and check constants carefully. The final question distinguishes two exceptional parameter values.
Choose k and h so the two equations represent the same line.
x + 3y = 4
2x + ky = h
7. Cost and Tariff Modelling
Translate receipts and pricing rules into equations. The final task changes the composition of a purchase.
Two snacks and one juice cost ₹64. One snack and one juice cost ₹40. Find each price.
8. Age Timeline Investigator
Apply each ratio at the correct time. Move both ages forward or backward by the same number of years.
Two siblings have total age 29 years and age difference 7 years. Find their present ages.
9. Digit Code Detective
Translate place value correctly. The final question requires you to recognise and resolve an ambiguity.
A two-digit number has digit sum 9. Its tens digit is three greater than its units digit. Find the number.
10. What Changes and What Stays Fixed
Study changes directly instead of repeatedly solving from the beginning. Use signed changes for increases and decreases.
The original pair is x + y = 6 and x − y = 2. Increase only the first right side by 2. Find the new solution.
Original: x + y = 6
Original: x − y = 2
About This Class 10 Linear Equations Worksheet
Read the NCERT Class 10 Maths Chapter 3 practice guide
This Pair of Linear Equations in Two Variables Class 10 worksheet combines written practice with interactive revision. Use the existing worksheet download option on this page for notebook work, then use the online quiz and activities to check your understanding.
A common solution must satisfy both equations. The graphical method makes this visible: intersecting lines have one common point, distinct parallel lines have none, and coincident lines share all their points.
When solving by substitution, isolate a variable carefully and preserve brackets during replacement. In the elimination method, multiply every term of an equation by the chosen factor. A correct operation on the left side must also be applied to the right side.
For consistency questions, proportional coefficients do not automatically mean infinitely many solutions. Compare the constants as well. If a coefficient ratio would involve division by zero, compare equivalent equations or cross-products instead.
The Class 10 Maths Chapter 3 activities include financial models, age relationships and digit problems. Define the unknowns with their units before forming equations. An algebraic answer must also fit the context: a digit must be an integer from 0 to 9, and a present age must be meaningful.
The final question in each revision set adds an extra reasoning demand, such as recovering a parameter, detecting insufficient information or predicting a change. These are original practice tasks rather than questions labelled as previous year board questions.
Use the separate Linear Equations notes and mind map for concept revision. Return to this worksheet to apply the ideas, review incorrect steps and verify solutions in both original equations.
Class 10 Linear Equations Extra Practice
Complete these five additional questions independently before checking.
1. Solve a New Pair
Enter your answer after completing the working in your notebook.
Solve 5x + 2y = 26 and 3x − 2y = 6.
2. Check Inconsistency
Enter your answer after completing the working in your notebook.
Find k so 7x − 3y = 10 and 14x + ky = 25 are inconsistent.
3. Recover a Constant
Enter your answer after completing the working in your notebook.
Find h so x − 4y = 3 and 5x − 20y = h have infinitely many solutions.
4. Work with New Variables
Enter your answer after completing the working in your notebook.
Solve 2u + 3v = 1 and 3u − 2v = 8.
5. Recover Two Coefficients
Enter your answer after completing the working in your notebook.
The ordered pair (−2, 3) solves px + y = 11 and x + qy = 7. Find p and q.
Linear Equations Revision Tips for Students
- Define both variables before forming a mathematical model.
- Keep equations in a consistent form when comparing coefficients.
- Multiply the constant term when multiplying an equation.
- Use brackets when subtracting an entire equation.
- Interpret a contradiction as no solution, not as zero values for the variables.
- Interpret an identity carefully: it does not determine a unique ordered pair.
- Verify your answer in both original equations.
- Check units and restrictions in age, cost and digit questions.
Tips for Parent and Teacher Support
- Ask the student to explain why the chosen operation preserves the solution.
- Connect each graph with its corresponding algebraic conclusion.
- Ask what additional information would make an underdetermined problem solvable.
- Use the five-question sets for short revision sessions and discuss the final reasoning task.
Pair of Linear Equations Class 10 FAQs
What is a pair of linear equations in two variables?
It consists of two linear equations involving the same two unknowns. A solution must satisfy both equations simultaneously.
How do I choose between substitution and elimination?
Substitution is convenient when a variable is already isolated or has coefficient 1. Elimination is often convenient when coefficients can easily be made equal or opposite. Either method should give the same solution.
What do consistent and inconsistent mean?
A consistent pair has at least one common solution. It may have one solution or infinitely many. An inconsistent pair has no common solution.
How do graphs show the number of solutions?
Intersecting lines have one common solution. Distinct parallel lines have no solution. Coincident lines have infinitely many solutions.
What does an equation such as 0 = 5 mean during elimination?
It is a contradiction. If your operations were correct, the original pair is inconsistent. It does not mean that both variables are zero.
Does 0 = 0 give the values of x and y?
No. It is an identity. When one equation reduces to the other, the pair has infinitely many solutions along their common line.
How do I solve questions involving a parameter?
Use the required relationship between the two lines. For coincident lines, the entire equations must be proportional. For parallel distinct lines, the variable terms are proportional but the constants do not have the same multiplier.
How do I form equations for age problems?
Define present ages first. Add the same number of years to both ages for a future condition and subtract the same number for a past condition. Apply each ratio to the ages at that particular time.
How do I write equations for a reversed two-digit number?
If x is the tens digit and y is the units digit, the number is 10x + y. Its reversal is 10y + x. Check the resulting digits against the question’s restrictions.
Can I practise several questions in the same activity?
Yes. Every game and HOTS activity has five questions. Previous Question and Next Question retain your entries while you work through the set.
Revise with the Linear Equations Online Quiz for Class 10
Use the quiz to identify a skill to revisit, complete its five-question activity and explain your method before attempting the quiz again.
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