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### Course: Operations and Algebraic Thinking 227-228>Unit 4

Lesson 5: Systems of equations word problems

# 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
• 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.
• 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.
• 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.
• Who else got this the moment they saw this?