Question 1097062: 1/2x + 3y = 2
ax -12y = -8
in this system of equations a is a constant.If the system has infinite solutions, what is the value of a?
Answer by ikleyn(52790)   (Show Source):
You can put this solution on YOUR website! .
a = -2.
It is the only value of "a", which makes the coefficients of the second equation proportional to the coefficients of the second equation,
as well as the right sides proportional with the same proportionality coefficient.
It is the necessary and sufficient condition for the given system of equations to have infinitely many solutions.
See the lesson
- Geometric interpretation of the 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".
Save the link to this online textbook together with its description
Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
to your archive and use it when it is needed.
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