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# Systems of equations with elimination: coffee and croissants

Sal solves a word problem about the price of coffee and croissant by creating a system of equations and solving it. Created by Sal Khan.

## Want to join the conversation?

• I've mastered this skill before and watched each video like 5,000,000 times ,but I got it wrong on a mastery and now i can't seem to get ANY of the questions right. Does anyone have any tips ?
• THIS IS GOING TO BE LONG..... I'll vote up your question.
So, before I get all scientific. That happened to me too! So, you mastered tis skill already, and watched it like 5,000,000 times, right. Well, what happens in your brain is all that information is getting stored. When, you watched it a lot and mastered the skill, the brain says " Okay, empinda knows this." And stops receiving information, and the the other things that you learned are disappearing, because you are practicing it too much. Now, that doesn't work for everything you study., What do you need too do in order to walk? Well, you have to know how to stand up, and move. That is simple so the brain does not forget about it, even if you practice it 5,00,000 times, you do it every single day, so the brain knows you need this, but solving equations you have to set up the equation, cancel it out, plug it in, and solve, etc. so, everytime you solve equation, your brain goes though all that, and soon your brain can't take it so, it disappears. And you probably learned more stuff after you watched it 5,000,000 times so as new stuff come in old stuff go out. Simple stuff, or important stuff don't go out.
Tip: don't study it that much, or find out a easier way!
• Couldn't you just look at it and say: 5.3 * 2 is not equal to 14!
• Of course you could, but that wouldn't be using a system of equation... I have travelled to Paris and this will happen to you.
• I’m sad you spent so much time on these really easy problems and hardly any time on the very difficult distance/ & rate problems. I struggle with distance and rate problems but you have many more examples of the much simpler problems. Why is that?
• Well, don't hesitate to try mastery challenge even if you never have seen similar problem, and even if you can't solve a hard problem -- at least try first, and then read the solution, there are quiet comprehensible explanation.
I watch this video just for energy points, and I rely only on tests, and I have seen a lot of distance & rate problems there, many of them I couldn't solve with the very first attempt.
• Can I call this system of equations "inconsistent" ?
• Yes, this system of equations is inconsistent. The slope of both lines is -1. But the y-intercepts are different. When graphed this will produce two parallel lines. Since parallel lines will never intersect, we call this an inconsistent system.
• How did 14 become 10.60?
• 14 didn't become 10,60.
We're comparing two situations with the same variable so it can be a little bit tricky but if it can help you :

Cup of coffee bought by you : X1
Croissant bought by you : Y1
Cup of coffee bought by the local : X2
Croisant bought by the local: Y2

You know that X2 + Y2 = 5,30
and : 2x1 + 2y1 = 14

You want to know if you paid the same price as the local. To verify this, X1 should = x2 and y1 should = y2, or in the video we say 2x1 = 2x2 and 2y1 = 2y2.
We then put two DIFFERENT equation to see if we can conclude something about it.
• In the problem I think it should be worded differently. Like I paused the video and tried it and I said no not possible cause it seems like that it says one coffee and one croissant for 5.3 euros. Not total of 5.3 euros. Or am I reading this wrong?
• So how did you interpret the statement "a cup or coffee and a croissant for 5.3 euros"? I would have seen this and immediately said let f be coffee and c be croissant, so 1f + 1c = 5.3. And often is an addition word in Math. Yes total would have been clearer but I cannot figure out any alternate interpretation.
• why wouldnt u just ask how much it costed
• Because then it wouldn't be a math problem.
(1 vote)
• this is so easy problem no need to solve. just a trick is needed. you just look at it and say (5.3) * 2 is not equal to 14.