Linear Equations in One Variable 8 Mathematics — Revision Notes
Linear equations in one variable are equations with the variable appearing to the first power, solved by isolating the variable. They form the foundation f
TL;DR: Linear equations in one variable are equations with the variable appearing to the first power, solved by isolating the variable. They form the foundat…
Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated
Linear equations in one variable are equations with the variable appearing to the first power, solved by isolating the variable. They form the foundation f
Key Points to Remember
- A linear equation in one variable has the form ax + b = 0, where a and b are constants and a ≠ 0
- The solution of an equation is the value of the variable that makes the equation true
- Equivalent equations have the same solution and can be obtained by adding or subtracting the same quantity from both sides
- Adding or subtracting the same quantity from both sides maintains equality
- Multiplying or dividing both sides by the same non-zero quantity maintains equality
- Transposition is moving a term from one side to the other by reversing its sign
- Linear equations can model real-world situations like distance, speed, age, and cost problems
- To solve, use inverse operations to isolate the variable on one side of the equation
- Check solutions by substituting back into the original equation
- Equations can have one solution, no solution, or infinitely many solutions
- Fractions in equations can be eliminated by multiplying all terms by the least common denominator
- Variables on both sides require moving variable terms to one side and constants to the other
Important Formulas
- ax + b = 0, Solution: x = -b/a
Key Terms
- Linear Equation: Equation where the variable appears to the first power and can be written as ax + b = 0
- Solution: The value of the variable that satisfies the equation and makes both sides equal
- Equivalent Equations: Equations that have the same solution
- Transposition: Moving terms between sides of an equation by reversing their operation
- Inverse Operation: Operation that reverses another operation, such as subtraction reversing addition
- Variable: Symbol representing an unknown quantity in an equation
Frequently Asked Questions
How do you solve a linear equation with variables on both sides?
Collect all variable terms on one side using transposition, then collect constant terms on the other side. Finally, divide both sides by the coefficient of the variable to isolate it
Why do we check solutions in linear equations?
Checking solutions by substituting back into the original equation verifies that no errors were made during solving and that the value truly satisfies the equation
How do you eliminate fractions in linear equations?
Multiply all terms in the equation by the least common multiple of all denominators to convert fractions to integers, making the equation easier to solve
More 8 Mathematics Revision Notes
🤖 Stuck on any of these? Ask Syllab's free AI Tutor to explain step by step →