SOLUTION: Hello! I am not very good with a system of equations, here is one of the problems that I am having trouble with. Find a value for a and b so that the system has infinitely many

Algebra.Com
Question 1143517: Hello! I am not very good with a system of equations, here is one of the problems that I am having trouble with.
Find a value for a and b so that the system has infinitely many solutions.
y = (2/3)x - 5
y = ax + b
Thanks!

Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
First equation represents straight line with the slope  and y-intercept of -5.


Second equation represents straight line with the slope "a" and y-intercept b


If you take  a=   and  b= -5,  the second equation will represent the same straight line as the first equation.


So, the system will have INFINITELY MANY solutions.


Or, simply, if a= ,  b= -5,  the two equation will be IDENTICAL and, therefore, the system will have 
infinitely many solutions.


So, your answer is  a=  ,  b= -5.

-----------------

To get a solid base in your knowledge, look into 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".

If you want to learn the subject, read the lessons from this topic and become an expert.
Consider these lessons as your textbook, handbook, guide, tutorials and (free of charhe) home teacher.


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.




RELATED QUESTIONS

Hello! I am not very good with a system of equations, here are another one of the... (answered by greenestamps)
i am having problems with solving dividing equations here is one of the problems i dont... (answered by fractalier)
Hi, I am having trouble with my homework. My teacher assigned some problems to solve for... (answered by stanbon,richard1234)
Hi, I am having trouble with my homework. My teacher assigned some problems to solve for... (answered by rfer)
hello my name is lisa, how are you? I am having trouble with a couple problems but some i (answered by nerdybill)
Hello there! I am having trouble with rate problems and how to solve them. here is one of (answered by stanbon,ikleyn)
Hello. I am having problems with some problems. I was able to locate some on your site... (answered by venugopalramana)
hello i am an eight grader and i am having a hard time with quadratic equations they... (answered by Edwin McCravy)
500 tickets for prizes are sold for $2 each. Five prizes will be awarded – one for $300,... (answered by stanbon)