Linear algebraic equations with two variables

Linear equations with two variables are as follows:

15x + 7y = 52

To solve such a system of simultaneous equations such as

15x + 7y = 52-----------------------1
5x + 3y = 18------------------------2

We can do as follows:

Method-1:
After Multiplying equation-2 with "3", we will get


15x + 7y = 52-----------------------1
3x(5x + 3y = 18)------------------------3

=>

15x + 7y = 52-----------------------1
15x + 9y = 54------------------------3

By subtracting these two equation, we get
 15x + 7y =  52
-15x - 9y = -54
-----------------
0 -2y = -2
=> y = -2/-2
=> y = 1

By putting this value of "y" in equation-1, we get
15x + 7y = 52
=> 15x + 7(1) = 52
=> 15x = 52-7
=> 15x = 45
=> x = 45/15 = 3

So, x = 3

Method-2:

15x + 7y = 52-----------------------1
5x + 3y = 18------------------------2

Take equation-2
5x + 3y = 18
=> x = (18-3y)/5

By putting this value of "x" in equation-1, we will get

15((18-3y)/5) + 7y = 52
=> 54-9y + 7y = 52
=> 54-2y = 52
=> -2y =-2
=> y = 1

By putting this value of "y" in equation-2, we get

x = (18-3)/5 = 15/5 = 3
=> x = 3

Further Reading:
Cracking the GRE, 2010 Edition (Graduate School Test Preparation)

Kaplan GRE Exam Vocabulary in a Box

Barron's GRE

Kaplan GRE Exam 2010-2011 Premier with CD-ROM (Kaplan GRE Premier Program (W/CD))

Kaplan GRE Exam 2010: Strategies, Practice, and Review

Crash Course for the GRE, 3rd Edition (Graduate School Test Preparation)