2. Linear Equations

Concepts Covered
Simple linear Equations, equations of the first order with one, two or three variables are tested in GMAT Problem Solving and Data Sufficiency sections of the GMAT CAT Test. 4GMAT's GMAT Math Lesson Book in this chapter covers the following concepts:

1. Definition of simple equation and degree of equation
2. Method to solve equations
3. Definition of linear equation
4. Illustrative examples to explain the above concepts
5. Definition of independent equation, dependent equation, quadratic equation, linear equation in two variables
6. Introduction to the concept of system of linear equations and the two methods to solve simultaneous linear equations, namely, solving by substitution and solving by elimination
7. Different types of solutions to a system of linear equations
8. Special cases in linear equations
9. 11 solved examples that would help understand the concepts explained in the chapter. Includes word problems.
10. 8 exercise problems with the answer key and also explanatory answers

Here is an example of a typical solved example in this chapter.
Sample Question
Question
Solve the following system of equations
5x + 4y -z = 26; 3x + y + z = 5; -2x + 5y - 2z = 19

Explanatory Answer
5x + 4y - z = 26 (1)
3x + y + z = 5 (2)
-2x + 5y - 2z = 19 (3)

Adding equations (1) and (2), we get 8x + 5y = 31 (4)
Multiplying equation (2) by 2 and adding with equation (3), we get ; 4x + 7y = 29 (5)
Multiplying equation (5) by 2 and deducting it from equation (4), we get y =3
Substituting y = 3 in equation (5), we get x = 2
Substituting values of x and y in equation (1), we get z = -4