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)