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Linear Equations

Linear Equations

MODULES

Basics of Equations
Graph, Dependent & Inconsistent Equations
Solving Equations
Age, Digits & Fraction Based Questions
Wrong Calculation and Exam Based Questions
Integer Solutions
2 Equations & 3 Variables
Items Measured in Groups of 2 or more
Transposed & Multiple Variables
Past Questions

CONCEPTS & CHEATSHEET

Concept Revision Video

SPEED CONCEPTS

Linear Equations 1
-/10
Linear Equations 2
-/10

PRACTICE

Linear Equations : Level 1
Linear Equations : Level 2
Linear Equations : Level 3
ALL MODULES

CAT 2025 Lesson : Linear Equations - Concepts & Cheatsheet

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Note: The video for this module contains a summary of all the concepts covered in this lesson. The video would serve as a good revision. Please watch this video in intervals of a few weeks so that you do not forget the concepts. Below is a cheatsheet that includes all the formulae but not necessarily the concepts covered in the video.

   8. Cheatsheet

111) A linear equation is an equation containing one or more variables, where the power of each of the variables in the equation is 111.

222) An equation remains the same if the same number is added, subtracted, multiplied, divided or raised as the power on both sides of the equation.

333) We need n\bm{n}n consistent and independent equations to solve for n\bm{n}n variables.

444) Dependent equations have infinite solutions and inconsistent equations have no solutions.

555) Solving 2\bm{2}2 Variables

Subtraction Method

111) Upon identify a variable to be eliminated, identify the LCM of their coefficients in the 222 equations, ignoring the positive/negative sign.
222) We multiply or divide the entire equations by constants such that the LCM becomes the coefficients of the selected variable.
333) We now add or subtract the two equations (depending on the sign) to eliminate 111 variable.
444) We are now left with 111 equation containing only 111 variable. Upon solving this variable, we
substitute this in either of the two equations to find the value of the other variable.

Substitution Method

111) In one of the equations, express one variable in terms of the other.
222) Substitute this in the other equation to get 111 equation with 111 variable.
333) Solve for this and substitute in either equation to find the other variable.

666) Solving 3\bm{3}3 Variables

111) Follow the elimination approach as detailed above to eliminate 111 variable from 222 pairs of
equations, say equations A and B and equations B and C.
222) We now have 222 equations with the same 222 variables each.
333) We solve this as explained under eliminations approach.

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