Linear Equations is an important maths topic for school exams and quantitative aptitude. It appears in SSC, banking, railway, state exams, entrance exams and placement tests. The topic becomes easy when the meaning, formula and common question types are learned together.
This tutorial explains linear equations in simple language with definitions, formulas, shortcut tricks, solved examples, practice questions, answers, common mistakes and FAQs. The aim is to help students understand the topic instead of only memorising formulas.
What Is Linear Equations?
A linear equation is an equation in which the highest power of the variable is one. It represents a straight-line relation.
Important Terms
| Point | Details |
|---|---|
| Variable | Unknown value such as x |
| Coefficient | Number multiplied with variable |
| Constant | Fixed number |
| Equation | Statement with equal sign |
| Solution | Value that satisfies equation |
Important Formulas
| Point | Details |
|---|---|
| One variable form | ax + b = c |
| Solution | x = (c – b)/a |
| Two variable form | ax + by = c |
| Slope intercept form | y = mx + c |
| Check | Substitute value in equation |
Step-by-Step Method
- Collect variable terms on one side.
- Collect constants on other side.
- Perform inverse operations.
- Find variable value.
- Substitute answer to check.
Shortcut Tricks
- Do same operation on both sides.
- Move term by changing sign.
- Remove brackets first.
- Clear fractions by multiplying LCM.
- Check solution in original equation.
Common Question Types
| Point | Details |
|---|---|
| One variable | Find x |
| Two variables | Find ordered pair or relation |
| Word problem | Form equation |
| Fraction equation | Clear denominator |
| Graph | Straight line |
Solved Examples
Example 1
Solve x + 5 = 12.
x = 7.
Example 2
Solve 2x = 18.
x = 9.
Example 3
Solve 3x – 4 = 11.
3x = 15, x = 5.
Example 4
If 2x + 3 = 9, find x.
2x = 6, x = 3.
Example 5
Check x=4 in x+6=10.
4+6=10, so correct.
Government Exam Style Questions
Question 1
A number plus 8 is 20. Find number.
Let number be x. x + 8 = 20, so x = 12.
Convert words into equation.
Question 2
Solve 5x – 7 = 3x + 9.
2x = 16, x = 8.
Bring variable terms together.
Question 3
Solve x/3 + 2 = 5.
x/3 = 3, so x = 9.
Use inverse operation.
Common Mistakes
- Changing side without changing sign.
- Dividing only one side.
- Not removing brackets.
- Ignoring negative signs.
- Not checking answer.
Practice Questions
- Solve x+3=10.
- Solve 2x=14.
- Solve 3x-5=10.
- Solve x/2=8.
- Solve 4x+1=17.
- Solve 5x=0.
- Solve x-9=2.
- Solve 2x+3=x+8.
- Number plus 5 is 13.
- Twice number is 18.
Answers to Practice Questions
- 7
- 7
- 5
- 16
- 4
- 0
- 11
- 5
- 8
- 9
Frequently Asked Questions
What is linear equation?
An equation with highest variable power one.
What is variable?
An unknown value.
How to solve linear equation?
Use inverse operations to isolate variable.
Can linear equation have two variables?
Yes, such as ax + by = c.
How to check answer?
Substitute value in original equation.
Revision Notes
Linear equations are solved by isolating the variable and keeping both sides balanced.
For quick revision, write the formula, solve one direct example, and then solve one word problem. This method helps in remembering the concept during exams.
Conclusion
Linear equations become easy when every operation is done equally on both sides.
Additional Exam Notes
Linear Equations questions should be solved by first writing the known values and then selecting the correct rule. Do not start calculation before checking what the question is asking. Many mistakes happen because students use the correct formula for the wrong quantity.
When practising, solve questions in levels. Start with direct formula use, then move to mixed examples, and finally solve exam-style questions with a timer. This builds accuracy first and speed later.
Always check the final answer. The answer should match the unit, condition and range of the question. A length cannot be negative, an angle should match the triangle condition, and a discount or interest answer should be based on the correct value.
Additional Exam Notes
Linear Equations questions should be solved by first writing the known values and then selecting the correct rule. Do not start calculation before checking what the question is asking. Many mistakes happen because students use the correct formula for the wrong quantity.
When practising, solve questions in levels. Start with direct formula use, then move to mixed examples, and finally solve exam-style questions with a timer. This builds accuracy first and speed later.
Always check the final answer. The answer should match the unit, condition and range of the question. A length cannot be negative, an angle should match the triangle condition, and a discount or interest answer should be based on the correct value.
Additional Exam Notes
Linear Equations questions should be solved by first writing the known values and then selecting the correct rule. Do not start calculation before checking what the question is asking. Many mistakes happen because students use the correct formula for the wrong quantity.
When practising, solve questions in levels. Start with direct formula use, then move to mixed examples, and finally solve exam-style questions with a timer. This builds accuracy first and speed later.
Always check the final answer. The answer should match the unit, condition and range of the question. A length cannot be negative, an angle should match the triangle condition, and a discount or interest answer should be based on the correct value.
Additional Exam Notes
Linear Equations questions should be solved by first writing the known values and then selecting the correct rule. Do not start calculation before checking what the question is asking. Many mistakes happen because students use the correct formula for the wrong quantity.
When practising, solve questions in levels. Start with direct formula use, then move to mixed examples, and finally solve exam-style questions with a timer. This builds accuracy first and speed later.
Always check the final answer. The answer should match the unit, condition and range of the question. A length cannot be negative, an angle should match the triangle condition, and a discount or interest answer should be based on the correct value.
Additional Exam Notes
Linear Equations questions should be solved by first writing the known values and then selecting the correct rule. Do not start calculation before checking what the question is asking. Many mistakes happen because students use the correct formula for the wrong quantity.
When practising, solve questions in levels. Start with direct formula use, then move to mixed examples, and finally solve exam-style questions with a timer. This builds accuracy first and speed later.
Always check the final answer. The answer should match the unit, condition and range of the question. A length cannot be negative, an angle should match the triangle condition, and a discount or interest answer should be based on the correct value.
Additional Exam Notes
Linear Equations questions should be solved by first writing the known values and then selecting the correct rule. Do not start calculation before checking what the question is asking. Many mistakes happen because students use the correct formula for the wrong quantity.
When practising, solve questions in levels. Start with direct formula use, then move to mixed examples, and finally solve exam-style questions with a timer. This builds accuracy first and speed later.
Always check the final answer. The answer should match the unit, condition and range of the question. A length cannot be negative, an angle should match the triangle condition, and a discount or interest answer should be based on the correct value.
Additional Exam Notes
Linear Equations questions should be solved by first writing the known values and then selecting the correct rule. Do not start calculation before checking what the question is asking. Many mistakes happen because students use the correct formula for the wrong quantity.
When practising, solve questions in levels. Start with direct formula use, then move to mixed examples, and finally solve exam-style questions with a timer. This builds accuracy first and speed later.
Always check the final answer. The answer should match the unit, condition and range of the question. A length cannot be negative, an angle should match the triangle condition, and a discount or interest answer should be based on the correct value.
Additional Exam Notes
Linear Equations questions should be solved by first writing the known values and then selecting the correct rule. Do not start calculation before checking what the question is asking. Many mistakes happen because students use the correct formula for the wrong quantity.
When practising, solve questions in levels. Start with direct formula use, then move to mixed examples, and finally solve exam-style questions with a timer. This builds accuracy first and speed later.
Always check the final answer. The answer should match the unit, condition and range of the question. A length cannot be negative, an angle should match the triangle condition, and a discount or interest answer should be based on the correct value.
Additional Exam Notes
Linear Equations questions should be solved by first writing the known values and then selecting the correct rule. Do not start calculation before checking what the question is asking. Many mistakes happen because students use the correct formula for the wrong quantity.
When practising, solve questions in levels. Start with direct formula use, then move to mixed examples, and finally solve exam-style questions with a timer. This builds accuracy first and speed later.
Always check the final answer. The answer should match the unit, condition and range of the question. A length cannot be negative, an angle should match the triangle condition, and a discount or interest answer should be based on the correct value.
Additional Exam Notes
Linear Equations questions should be solved by first writing the known values and then selecting the correct rule. Do not start calculation before checking what the question is asking. Many mistakes happen because students use the correct formula for the wrong quantity.
When practising, solve questions in levels. Start with direct formula use, then move to mixed examples, and finally solve exam-style questions with a timer. This builds accuracy first and speed later.
Always check the final answer. The answer should match the unit, condition and range of the question. A length cannot be negative, an angle should match the triangle condition, and a discount or interest answer should be based on the correct value.
Additional Exam Notes
Linear Equations questions should be solved by first writing the known values and then selecting the correct rule. Do not start calculation before checking what the question is asking. Many mistakes happen because students use the correct formula for the wrong quantity.
When practising, solve questions in levels. Start with direct formula use, then move to mixed examples, and finally solve exam-style questions with a timer. This builds accuracy first and speed later.
Always check the final answer. The answer should match the unit, condition and range of the question. A length cannot be negative, an angle should match the triangle condition, and a discount or interest answer should be based on the correct value.
Additional Exam Notes
Linear Equations questions should be solved by first writing the known values and then selecting the correct rule. Do not start calculation before checking what the question is asking. Many mistakes happen because students use the correct formula for the wrong quantity.
When practising, solve questions in levels. Start with direct formula use, then move to mixed examples, and finally solve exam-style questions with a timer. This builds accuracy first and speed later.
Always check the final answer. The answer should match the unit, condition and range of the question. A length cannot be negative, an angle should match the triangle condition, and a discount or interest answer should be based on the correct value.
Additional Exam Notes
Linear Equations questions should be solved by first writing the known values and then selecting the correct rule. Do not start calculation before checking what the question is asking. Many mistakes happen because students use the correct formula for the wrong quantity.
When practising, solve questions in levels. Start with direct formula use, then move to mixed examples, and finally solve exam-style questions with a timer. This builds accuracy first and speed later.
Always check the final answer. The answer should match the unit, condition and range of the question. A length cannot be negative, an angle should match the triangle condition, and a discount or interest answer should be based on the correct value.
Additional Exam Notes
Linear Equations questions should be solved by first writing the known values and then selecting the correct rule. Do not start calculation before checking what the question is asking. Many mistakes happen because students use the correct formula for the wrong quantity.
When practising, solve questions in levels. Start with direct formula use, then move to mixed examples, and finally solve exam-style questions with a timer. This builds accuracy first and speed later.
Always check the final answer. The answer should match the unit, condition and range of the question. A length cannot be negative, an angle should match the triangle condition, and a discount or interest answer should be based on the correct value.
Additional Exam Notes
Linear Equations questions should be solved by first writing the known values and then selecting the correct rule. Do not start calculation before checking what the question is asking. Many mistakes happen because students use the correct formula for the wrong quantity.
When practising, solve questions in levels. Start with direct formula use, then move to mixed examples, and finally solve exam-style questions with a timer. This builds accuracy first and speed later.
Always check the final answer. The answer should match the unit, condition and range of the question. A length cannot be negative, an angle should match the triangle condition, and a discount or interest answer should be based on the correct value.
Additional Exam Notes
Linear Equations questions should be solved by first writing the known values and then selecting the correct rule. Do not start calculation before checking what the question is asking. Many mistakes happen because students use the correct formula for the wrong quantity.
When practising, solve questions in levels. Start with direct formula use, then move to mixed examples, and finally solve exam-style questions with a timer. This builds accuracy first and speed later.
Always check the final answer. The answer should match the unit, condition and range of the question. A length cannot be negative, an angle should match the triangle condition, and a discount or interest answer should be based on the correct value.
Additional Exam Notes
Linear Equations questions should be solved by first writing the known values and then selecting the correct rule. Do not start calculation before checking what the question is asking. Many mistakes happen because students use the correct formula for the wrong quantity.
When practising, solve questions in levels. Start with direct formula use, then move to mixed examples, and finally solve exam-style questions with a timer. This builds accuracy first and speed later.
Always check the final answer. The answer should match the unit, condition and range of the question. A length cannot be negative, an angle should match the triangle condition, and a discount or interest answer should be based on the correct value.
Additional Exam Notes
Linear Equations questions should be solved by first writing the known values and then selecting the correct rule. Do not start calculation before checking what the question is asking. Many mistakes happen because students use the correct formula for the wrong quantity.
When practising, solve questions in levels. Start with direct formula use, then move to mixed examples, and finally solve exam-style questions with a timer. This builds accuracy first and speed later.
Always check the final answer. The answer should match the unit, condition and range of the question. A length cannot be negative, an angle should match the triangle condition, and a discount or interest answer should be based on the correct value.
Additional Exam Notes
Linear Equations questions should be solved by first writing the known values and then selecting the correct rule. Do not start calculation before checking what the question is asking. Many mistakes happen because students use the correct formula for the wrong quantity.
When practising, solve questions in levels. Start with direct formula use, then move to mixed examples, and finally solve exam-style questions with a timer. This builds accuracy first and speed later.
Always check the final answer. The answer should match the unit, condition and range of the question. A length cannot be negative, an angle should match the triangle condition, and a discount or interest answer should be based on the correct value.
Additional Exam Notes
Linear Equations questions should be solved by first writing the known values and then selecting the correct rule. Do not start calculation before checking what the question is asking. Many mistakes happen because students use the correct formula for the wrong quantity.
When practising, solve questions in levels. Start with direct formula use, then move to mixed examples, and finally solve exam-style questions with a timer. This builds accuracy first and speed later.
Always check the final answer. The answer should match the unit, condition and range of the question. A length cannot be negative, an angle should match the triangle condition, and a discount or interest answer should be based on the correct value.
Additional Exam Notes
Linear Equations questions should be solved by first writing the known values and then selecting the correct rule. Do not start calculation before checking what the question is asking. Many mistakes happen because students use the correct formula for the wrong quantity.
When practising, solve questions in levels. Start with direct formula use, then move to mixed examples, and finally solve exam-style questions with a timer. This builds accuracy first and speed later.
Always check the final answer. The answer should match the unit, condition and range of the question. A length cannot be negative, an angle should match the triangle condition, and a discount or interest answer should be based on the correct value.
Additional Exam Notes
Linear Equations questions should be solved by first writing the known values and then selecting the correct rule. Do not start calculation before checking what the question is asking. Many mistakes happen because students use the correct formula for the wrong quantity.
When practising, solve questions in levels. Start with direct formula use, then move to mixed examples, and finally solve exam-style questions with a timer. This builds accuracy first and speed later.
Always check the final answer. The answer should match the unit, condition and range of the question. A length cannot be negative, an angle should match the triangle condition, and a discount or interest answer should be based on the correct value.