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### Course: Algebra basics>Unit 5

Lesson 1: Systems of equations intro

# Systems of equations: trolls, tolls (2 of 2)

Solving the system of equations visually. Now we can save the prince/princess. Created by Sal Khan.

## Want to join the conversation?

• I was wondering how many different ways can you solve this question (the one it asks in the video) ?
• Also by matrices after some more levels of math practice.
• In the last video sal said that you have to solve the riddle in under 10 minutes, it takes 11 for Sal to solve it. So we are drowning in the river
• Watch the video in faster playback then you could warp time and the troll won't drown you.
• imagine being the troll waiting as sal explains your riddle
• Troll:
Hmm...
Oh... So that's how you solve it...
Should I just throw him off the bridge...
It takes too much time...
Oh is it about to end?
• Is there another method to find the answer than drawing the graphs?
• Well, yes.
Assume that all of the 900 dollar bills are all 5 dollars bills.
-> the total amount of money is 900*5=4500 dollar
However, the real amount of money is \$5500. Therefore, the difference is 5500-4500=1000 dollar.
The difference between a \$5 bill and a \$10 bill is \$5.
-> the number of \$10 bill is 1000/5=200 bills.
-> the number of \$5 bill is 900-200=700 bills.
• sal has godlike drawing skills
• Could someone elaborate on this a little bit more? It seems to me like a guess work. Isn't it just as feasible that the troll has 702 \$5 bills and 199 \$10 bills? If not, why not? How does the two graphs intersecting prove the different configurations of \$10 and \$5 bills that the troll has? I need someone to walk me through the logical reasoning and steps behind this.
• 702 + 199 = 901 bills instead of 900 as required by the problem. If you try 701 and 199 which does equal 900 bills, the money woud be 701*5 + 199*10 = 5495, and 699 and 201 would give 699*5 + 201*10 = 5505, both of which are close to 5500, but not exact.
The idea is that for every variable you have, in order to find a unique solution, you have to have a unique equation (not the same slope) for the number of variables. The place of intersection is a value of (x,y) that uniquely works for both equation, the only point that is on both lines.
• can this be solved without graph?
(1 vote)
• Yes, systems can be solved graphically, but they can also be solved using methods of elimination, substitution, or a combination of both. Very rarely will graphically solving be handy because of human errors when drawing and the time it takes to graph.
• I am here by myself. Look, math is a vital part in life and it can be required in numerous fields. Thus, if you want to be a great specialist you need math.