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(52776)   (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.
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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.
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