BackALL MODULES
CAT 2025 Lesson : Linear Equations - Concepts & Cheatsheet
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
) A linear equation is an equation containing one or more variables, where the power of each of the variables in the equation is .
) 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.
) We need consistent and independent equations to solve for variables.
) Dependent equations have infinite solutions and inconsistent equations have no solutions.
) Solving Variables
Subtraction Method
) Upon identify a variable to be eliminated, identify the LCM of their coefficients in the equations, ignoring the positive/negative sign.
) We multiply or divide the entire equations by constants such that the LCM becomes the coefficients of the selected variable.
) We now add or subtract the two equations (depending on the sign) to eliminate variable.
) We are now left with equation containing only variable. Upon solving this variable, we
substitute this in either of the two equations to find the value of the other variable.
Substitution Method
) In one of the equations, express one variable in terms of the other.
) Substitute this in the other equation to get equation with variable.
) Solve for this and substitute in either equation to find the other variable.
) Solving Variables
) Follow the elimination approach as detailed above to eliminate variable from pairs of
equations, say equations A and B and equations B and C.
) We now have equations with the same variables each.
) We solve this as explained under eliminations approach.
) 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.
) We need consistent and independent equations to solve for variables.
) Dependent equations have infinite solutions and inconsistent equations have no solutions.
) Solving Variables
Subtraction Method
) Upon identify a variable to be eliminated, identify the LCM of their coefficients in the equations, ignoring the positive/negative sign.
) We multiply or divide the entire equations by constants such that the LCM becomes the coefficients of the selected variable.
) We now add or subtract the two equations (depending on the sign) to eliminate variable.
) We are now left with equation containing only variable. Upon solving this variable, we
substitute this in either of the two equations to find the value of the other variable.
Substitution Method
) In one of the equations, express one variable in terms of the other.
) Substitute this in the other equation to get equation with variable.
) Solve for this and substitute in either equation to find the other variable.
) Solving Variables
) Follow the elimination approach as detailed above to eliminate variable from pairs of
equations, say equations A and B and equations B and C.
) We now have equations with the same variables each.
) We solve this as explained under eliminations approach.
Want to read the full content
Unlock this content & enjoy all the features of the platform
Subscribe Now
