# Solving GMAT Questions with two linear equations and two unknowns

In order to solve such equations, you need at least 2 distinct equations involving these unknowns.

For example, if we are trying to solve for x and y, we won't be able to solve it using these 2 equations.

2x + y = 14
4x + y - 14 = 14 - y

Why?  Because the two equations on top are the same.  If you simplify the second equation, you get 4x + 2y = 28 which reduces to 2x + y = 14 - the same equation as the first.  If the two equations are the same, then there will be infinitely many values for x and y that will satisfy the equations.  For example, x = 2 and y = 10 satisfies the equation.  So does x = 4 and y = 8.  And so does x = 6 and y = 2.

In order to solve for an actual value of x and y, we need 2 distinct equations.

For example, if we had

2x + y = 14 --------(1)
x - y = 4 ----------(2)

Then from equation (2), we can get x = 4 + y and substitute that into equation (1) to get:
2(4 + y) + y = 14  We can then solve for y.  See if you got y = 2  Once you've got y = 2, you can substitute that into x= 4 + y to get x = 6.

An important lesson here is that you need as many distinct equations as you have variables.  So if you are doing a data sufficiency question, you can sometimes just note that as long as you have two distinct equations, you will be able to solve for x and y.  Disregard or other equivalent equations.

Sometimes, however, its possible for there to be no solution to the set of equations.  This occurs when one side of each equation is the same, but the other side is different.  For example,

2x + y = 14
2x + y = 0

has no solution.  Its like saying that the same steak costs \$14 and \$0 at the same restaurant.  Of course, the GMAT is not going to make it so obvious that the equations contradict each other.

Usually, you would have to simplify one of the equations to check if it is

1. the same same as the other equation, in which case, you have infinitely many solutions
2. the same as the other equation on one side, but different on the other side of the equal sign.  In this case, you have no solution
3. a distinct equation, in which case x and y has an exact value.

The GMAT might also require you to translate a word problem into a pair of simultaneous equations to solve.  Let's try this question from Grockit.

A package contains nothing but 35 DVDs and 15 videotapes. What is the total weight, in pounds, of the contents of the package?

(1) Each videotape weighs twice as much as each DVD.
If we let the weight of a DVD be x and a videotape be y, then according to this statement y = 2x
(2) The total weight of 2 of the videotapes and 2 of the DVDs is 1 pound.

Following the previous notation, 2y + 2x = 1

Author :

Grockit, an online test prep game, is the smartest way to study for your test. It's adaptive, fun and finds the right teacher for you. Grockit’s analytic capabilities and adaptive technology identifies students' strengths and weaknesses, focusing the student's study time.  Students can practice in adaptive solo games, play social learning games with peers, and work with experts that match their specific needs.

Essential GMAT Reading Comprehension Guide After reading F1GMAT’s Essential GMAT Reading Comprehension Guide, you will:

1. Complete GMAT RC Questions in less than 1 minute and 50 seconds
3. Take Notes Effectively
4. Collect and Interpret Facts
5. Speed up Summary Creation
6. Remember Information
7. Question the Author
8. Learn to Answer GMAT Reading Comprehension Title question
9. Learn to Answer GMAT Reading Comprehension Main Idea Question

10.Learn to Answer GMAT Reading comprehension Inference question

11. Learn to Answer GMAT Reading Comprehension Detail Question

12. Learn to Answer GMAT Reading Comprehension Purpose Question
12. Learn to Answer GMAT organization of passage Question
13. Learn to identify the style/tone or attitude of the author

Download Essential GMAT Reading Comprehension Guide (2019 Edition) (100+ New Questions)

Mastering GMAT Critical Reasoning After you read F1GMAT’s Mastering GMAT Critical Reasoning Guide, you will learn:

How to overcome flawed thinking in GMAT Critical Reasoning?

How to spot Inconsistencies in Arguments

How to eliminate out of scope answer choices using Necessary and Sufficient Conditions

How to Paraphrase GMAT Critical Reasoning Question

How to Answer Assumption Question Type

How to Answer Conclusion Question Type

How to Answer Inference Question Type

How to Answer Strengthen Question Type

How to Answer Weaken Question Type

How to Answer bold-faced and Summary Question Types

How to Answer Parallel Reasoning Questions

How to Answer the Fill in the Blanks Question

Download Mastering GMAT Critical Reasoning (2019 Edition) (25+ New Questions)

Get F1GMAT's Newsletters (Best in the Industry)
Included in the Newsletter:

• Ranking Analysis
• Post-MBA Salary Trends
• Post-MBA Job Function & Industry Analysis
• Post-MBA City Review
• MBA Application Essay Tips
• School Specific Essay Tips
• GMAT Preparation Tips
• MBA Admission Interview Tips
• School Specific Interview Tips
• Funding Guidance and
• Special Consultation Service (only for Subscribers)

Subscribe to F1GMAT's Newsletter