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# Systems of equations number of solutions: fruit prices (2 of 2)

Sal gives an example of a system of equations that has infinite solutions! Created by Sal Khan.

## Want to join the conversation?

• Not a question, just here to say it took me several videos to realise Arbegla is an anagram of Algebra facepalm
• I realised it very early(when your teacher takes 3 years to explain how x=1 and how alphabet went into math, you will remember the word algebra alright.
• I just realized that "Arbegla" was "Algebra" backwards!
• Hi,

Just to make sure I understand what is going on here:
Would it be correct to state that essentially you just had 1 equation? Which means this example is actually not a system of equation?

• Yes - Essentially the 2 equations are the same. If you take the 2nd equation: 6a+3b=15 and divide it by 3, you get the 1st equation 2a+b=5.
• How do we can explain inconsistency? What does it means?
• Simple inconsistency is not consistent. Consistent is when all the systems agree.
• How does the system of equations being consistent and having an infinite number of solutions make it dependent? And what would make a system independent?
• What is a system of equations?
• A system of equations is a group of equations that are grouped together that allow for easier solving for the variables they contain.

They look like this:
``2x + 3y = 184x - 10y = 9``

There can be as many equations and variables as you would like, or as many as the problem requires. Hopefully this answers your question sufficiently.
• Is it possible to use a proportion equation to solve these? These are tough and creating quite the obstacle for me haha
• What does Sal mean by infinite number of solutions and, how is this possible?
• When finding the solution to a system of 2 linear equations, we are finding the point(s) that the 2 lines have in common (where they overlap). There are 3 possible scenarios:
1) The 2 lines intersect. This means they share one point, which is defined as an ordered pair (x-value, y-value).
2) The 2 lines are parallel. In this scenario, parallel lines would never touch, so they have no points in common. This means the system has no solution, because there are no points in common.
3) The 2 equations can create the same line. This would mean that the lines share all their points. So, the solution to the system is all the points on the line, which would be an infinite set of ordered pairs.

Hope this helps.