SOLUTION: Consider the eqautions 3x+4y=7 and 6x+8y=13. Is the pair of equations consistent, inconsistent, or dependant?

Question 1077905: Consider the eqautions 3x+4y=7 and 6x+8y=13. Is the pair of equations consistent, inconsistent, or dependant?
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.

The pair of equations is inconsistent.


Indeed, the left sides of the equations are proportional with the proportionality coefficient 2 
( 2 is the ratio of coefficients of the second equation to that of the first equation).


At the same time, the right sides are NOT proportional with the same coefficient.


Therefore, the system HAS NO solutions.


In other words, it is INCONSISTENT.

See the lesson
- Geometric interpretation of a linear system of two equations in two unknowns
in this site.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic "Systems of two linear equations in two unknowns".

RELATED QUESTIONS
In the given system of equations is consistent and dependent, consistent and independent... (answered by venugopalramana)

Solve the system of equations: 6x-4y=-16 and 4y-6x=16 and is the system consistent or... (answered by mathgranny)

solve the system of equations by graphing and label consistent, inconsistent, dependant,... (answered by stanbon)

Solve the system of linear equations. Determine whether the system is consistent or... (answered by Alan3354)

For each system of equations, use the determinants (D and possibly D little y) to state... (answered by solver91311)

Determine whether the system is consistent, inconsistent, or dependent. 3x + 2y = 15 6x (answered by drk)

Determine whether the system is consistent, inconsistent, or dependent 3x+ 2y = (answered by John10)

Determine whether the system is consistent, inconsistent, or dependent. 3x + 2y = 15 6x (answered by jorel1380)

Graph each system of equations and find any solutions. Check your answers. Identify the... (answered by Fombitz)