# Math Book 1 : Linear Equations

Linear Equations is a topic from which you could expect 1 to 2 questions in the GMAT quant section. The concept is tested both in the problem solving format - mainly as a word problem - and in the data sufficiency format - mainly in testing your knowledge about unique solutions to a pair of linear equations. The topic is an important one.

Linear Equations

1

Book 1

## 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:- Definition of simple equation and degree of equation.
- Method to solve equations.
- Definition of linear equation.
- Illustrative examples to explain the above concepts.
- Definition of independent equation, dependent equation, and linear equation in two variables.
- 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.
- Different types of solutions to a system of linear equations.
- Special cases in linear equations.
- 3 illustrative examples and 13 solved examples that would help understand the concepts explained in the chapter. Includes word problems.
- 8 exercise problems with the answer key and also explanatory answers.
- 34 questions test on Linear and Quadratic equations as part of the work book.

## 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 the result 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

## Chapterwise details of 4GMAT's Math Lesson Books

**Math Lesson Book 1**

- Linear Equations
- Quadratic Equations
- Set Theory
- Sequences & SeriesDetails | Quiz
- Number Theory
- InequalitiesDetails | Quiz
- Functions

**Math Lesson Book 2**

- Descriptive StatisticsDetails
- Ratio ProportionDetails
- MixturesDetails
- InterestDetails
- Rates : Speed DistanceDetails
- Rates : RacesDetails
- Rates : Pipes CisternsDetails
- Rates : Work TimeDetails

**Math Lesson Book 3**

- PercentsDetails
- ProfitsDetails
- PermutationDetails
- ProbabilityDetails
- GeometryDetails
- Solid GeometryDetails
- Coordinate GeometryDetails

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