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# System of equations word problem: no solution

Systems of equations can be used to solve many real-world problems. In this video, we solve a problem about a toy factory. In this case, the problem has no viable solution, which means the information describes an impossible situation.

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• Ok. I understand that the scenario is imposible. According to previos vídeos there only could be 3 possible solutions graphing the system of equations. The only case with no solutions is represented by two parallel lines. Is this case graphed that way?
• It is exactly graphed that way; I used Desmos to input the equations and you can see that the lines are parallel: https://www.desmos.com/calculator/vkkpf2e7kw
• I did 14m+2w= -40 and got m= 24/28. Did i set this up incorrectly?
• Yes, sorry to say, you set it up incorrectly.
14m = total toys
2w = toys packed.
40 = toys remaining unpacked.
The key word is remaining. This is the result of a subtraction. As the workers pack the toys, they reduce the total toys. The 40 are the amount leftover where there weren't enough workers to pack them.
So, Sal's version: 14m - 2w = 40 is the equation you want.
OR, you can do: Total toys = Toys packed + Toys not yet packed. This creates the equation: 14m = 2w + 40.
Hope this helps.
• ok, I get how the linear equations work and how to get results out of systems of equations. but I dont know how to form/abstract an equation out of an real problem. how can I go on with the thought process?
• so if this problem was in the Systems of equations word problems below, HOW CAN WE SOLVE THIS?
• As noted in the video, this system has no solution. A solution to a system of equations is the point(s) that the 2 lines have in common. These lines are parallel. They never touch each other, so they share no points in common. This is why the system has no solution.
• At , we could also convert the equation 14m - 2w = 40 in terms of w and express it in the slope intercept form.

We can observe that it is w = 7m - 20 while our other equation is 7m - 8. Hence, we can see that these are parallel lines with different y-intercepts and thus will never intersect, giving us a system with no solutions
• At we got two equations 14M(Toys) - 2W(Toys) = 40 (Toys) and 7M(workes)-W(Workers)=8(workers). How we can subtract workers from toys ?
• I went back and watched the video, so I do not understand what do you mean by having toys and workers in parentheses. When do you think he subtracts workers from toys?
The equations say 14M (machines) - 2W(workers) = 40 (toys produced, not packed) and W (workers) = 7M (machines) - 8. For the first equation, you need at least 3 machines, so 14(3) = 42 which would mean 4 machines created 42 toys, then with one worker 2(1) = 2 would mean that one worker packed 2 toys, so 40 toys left unpacked. 4 machines would produce 56, and 8 workers would pack 16 toys, so you are consistently talking about toys either created by machines or packed by workers. The second equation gives a comparison of number of workers and machines and has nothing to do with toys at all.
• One mistake can change an entire answers
Orginally I had ---> 40=14m+2w, w=(7m)-8
I didnt subtract 2w from 14m and ended up getting
6 workers and 2 machines, which is a solution to this system, but its the wrong system.
• Are systems of equations always linear? If so, why?
• A system of equations whose left-hand sides are linearly independent is always consistent.
• in the first equation 14m gives the no of toys produced by each machine .
then in the second 7m gives the no of machines
how can we equate these two?