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# System of equations word problem: infinite solutions

Systems of equations can be used to solve many real-world problems. In this video, we solve a problem about a vegetable farmer. In this case, the problem has infinite solutions, which means there's not enough information to find a single solution.

## Want to join the conversation?

• Here graphically, infinite solutions means that the lines would be on top of one another?
• Yes. When solving a system of 2 equations, if your answer is infinite solutions, it means one line is on top of the other. Or, you can say, the 2 equations create the same line.
• What does it truly mean to to have infinite solutions in real life? Would it mean that no matter how many acres he has the equation would be true?
• Exactly. Basically meaning if there is a problem like 8x + 1 = 1 + 8x you can put anything in the X's and it would be the same. For the problem i explained (example), if you put 9 for x and add 1 to the 9, 10=10 so whatever you put for x it would work
• If we have infinite solution so why we say that every thing is possible even we can not solve a single question.
• Because somethings are not possible and that is the hard truth.
• when you have an infinite number of solutions the graphed lines are parallel to each other
(1 vote)
• Nope. In a system of equations, the solution is the point where the graphed lines intersect. Parallel lines never intersect, so they have zero solutions. Lines that are the same are always together, so those are the ones with infinite solutions.
• a problem which has infinite solutions doesn't always have to be 0=0 or can it be any integer=the same inter ex 8=8 9=9 10=10 right?
• Yes, if we get any statement that is always true, then there are infinitely many solutions.

Have a blessed, wonderful day!
• What would this mean in a real life scenario?
(1 vote)
• what happens when there are fractions instead of whole numbers?
like:
1/6x-3y=-58
5x+1/4y=65
• The easiest way to deal with it is to eliminate the fractions. You can multiply the 1st equation by 6:
6(1/6x) - 6(3y) = 6(-58)
You get: x - 18y = -348

For the 2nd equation, multiply it by 4 to eliminate the fraction.

One the fractions are gone, use elimination or substitution to solve the system.

Note: You can do the work keeping the fractions. It's just more work.

Hope this helps.
• so in these word equations would it be fair to say that if one equation and another equation are equal to a number and that if one equation is a multiple then you dont have to do any math/ saying that 12b + 16s is one equation and 3b + 4s is the other equation then its infinite.
• First off, you do not have equations, you have expressions. If you start with 3b+4s=6, if you multiply this whole equation by 4, you get 12b+16s=24, so you do in fact have infinite solutions. However, if it were any other number beside 24, for example 12b+16s=10, then they are parallel and have no solution.
• The sentence doesn't say that sometimes the farmer grews both spinach and broccoli, and sometimes just broccoli or spinach. You know last year the farmer grew at least 6 tons of broccoli per acre and 9 tons of spinach per acre. Is more correct to use the linear equation 6 (b + 1) + 9 (s + 1) = 93 , isn't it?
P.s. We don't have enough informations fguring out the solutions anyway, I know that. :P