 # Math Book 1: Linear Equations

Algebra and 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.

### 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. Wizako'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, and 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. 3 illustrative examples and 13 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.
11. 34 questions test on Linear and Quadratic equations as part of the work book.

Here is a typical solved example from this chapter.

### Sample Question

Solve the following system of equations
5x + 4y -z = 26; 3x + y + z = 5; -2x + 5y - 2z = 19

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)

Multiply equation (2) by 2 and add the result with equation (3)
6x + 2y + 2z = 10 ...... 2 * (2)
-2x + 5y - 2z = 19
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4x + 7y = 29 ...... (5)
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Multiply equation (5) by 2 and deduct equation (4) from the result
8x + 14y = 58 ...... 2 * (5)
8x + 5y = 31
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9y = 27
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Or y = 3

Substitute y = 3 in equation (5): x = 2
Substitute values of x and y in equation (1): z = -4

### Chapterwise details of Wizako's Math Lesson Books

Math Lesson Book 1

 1 Linear Equations Details 2 Quadratic Equations Details 3 Set Theory Details 4 Sequences & Series Details 5 Number Properties & Theory Details 6 Inequalities Details 7 Functions

Math Lesson Book 2

 1 Descriptive Statistics Details 2 Ratio Proportion Details 3 Mixtures 4 Interest 5 Rates: Speed Distance Details 6 Rates: Races Details 7 Rates: Work Time Details

Math Lesson Book 3

 1 Percents Details 2 Profits Details 3 Permutation Combination Details 4 Probability Details 5 Geometry Details 6 Solid Geometry 7 Coordinate Geometry Details