Shortcut Methods and Tricks for Numericals on System of Linear Equations:

1. JEE Main Level:

• Substitution Method: Substitute the value of one variable in terms of the other from one equation into another equation and simplify to solve for the remaining variable.

• Elimination Method (by addition/ subtraction): Add or subtract the equations in a way that eliminates one variable and solve the resulting equation for the remaining variable.

• Matrix Methods (Determinants and Cramer’s Rule): Use determinants to find the solutions of the system of linear equations when expressed in matrix form. Cramer’s Rule can also be applied for certain systems.

2. CBSE Board Level:

• Graphical Solution: For two equations with two variables, graph the equations and find the point of intersection, which represents the solution to the system.

• Substitution Method: Similar to JEE level, substitute the value of one variable in terms of the other from one equation into another and simplify to solve for the remaining variable.

• Elimination Method (by addition/ subtraction): As mentioned for JEE level, add or subtract equations to eliminate one variable and solve the resulting equation.

• Cramer’s Rule (for 2x2 systems): Despite being taught at JEE level, Cramer’s Rule can be applied to 2x2 systems for CBSE board level as well.

Remember to practice a variety of numerical problems regularly and gain proficiency in these shortcut methods to enhance your problem-solving skills and time management in exams.