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Graphical Systems Application Problem. Created by Sal Khan and Monterey Institute for Technology and Education.
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- why do you need a graph, it whould much easier to do it in your head?(17 votes)
- For this equation, yes it is way easier to do in your head. But much of what you'll do in stats or macroeconomics will be far more complicated. This is a just a simplified version so you learn the concept.(7 votes)
- Anyone else solve this in their head in the first minute? :) I sort of just did it logically, is Sal just trying to show us how to do it a different way?(7 votes)
- I can't figure out how to graph these equations, no matter how many videos I watch about this topic. Can anybody explain?(6 votes)
- To graph these system of equations, you have to graph the unknowns using the y intercept, and the coefficient of x to figure out how the graph grows. You graph the other equation overlapping the first equation on the graph, and the point where the two graphs intersect is the solution.(2 votes)
- Ok, so I think I'm getting it.
The easiest way is doing it with your head - since this is an easy question.
A more complicated way is to graph it...
But is there a way on solving it/finding a solution with just the equation?(4 votes)
- But sometimes in like Algebra 1, you learn parabolas and they are definitely harder to solve in your head and that is when you do the graphing method. But for problems like this I agree with you; algebraically it is much easier.(4 votes)
- At2:18, why is there -B on the right side?(4 votes)
- What is x + y =z(4 votes)
- doing the substitution method I get a=20 and b=30. Why?(4 votes)
- I think you may have mixed something up in your calculation.
A=B+10 Subsituting B+10 for A in the first equation,
(B+10)+B = 50 No subtract 10 from both sides
2B=40 Divide both sides by 2
Now put 20 in for B in A+B=50, so
I hope that helps(3 votes)
- I cannot seem to get the equations out of the word problem, any tips on easily finding it? ? ? ?(3 votes)
- What they ask you is unknown. Use letter to represent unknown.
Try to convert words into math expressions. "More by..." or "older by..." or "greater by .." means plus. "Less by.." means minus. "... times older" or "... in each" means multiply.
Hope this helps.(4 votes)
- At1:45, they say abby takes place of the y axis and ben takes places of the x axis, but why can't it be switched around, like instead abby takes of the x axis?(3 votes)
- We can switch it around, it doesn't matter. The only difference is that now 𝐵 is a function of 𝐴, so we would rewrite our equations as:
𝐵 = 𝐴 − 10
𝐵 = 50 − 𝐴
As we graph these two lines, we'll notice that they intersect at (30, 20), so Abby made $30 and Ben made $20.(4 votes)
- but cant you just 50-10, which is 40 and then divide it by 2 and you get 20? which is Ben's earnings?(3 votes)
Use graphing to solve the following problem. Abby and Ben did household chores last weekend. Together they earned $50, and Abby earned $10 more than Ben. How much did they each earn? So let's define some variables here. Let's let A equal Abby's earnings. And let's let B equal Ben's earnings. Then they tell us how these earnings relate. They first tell us that together they earned $50. So that statement can be converted mathematically into-- well, together, that means the sum of the two earnings. So A plus B needs to be equal to $50. Abby's plus Ben's earnings is $50. And then they tell us Abby earned $10 more than Ben. So we could translate that into Abby's earnings is equal to Ben's earnings plus 10. Abby earned $10 more than Ben. So we have a system of two equations and actually with two unknowns. And then they say, how much did each earn? So to do that, and they want us to solve this graphically. There's multiple ways to solve it, but we'll do what they ask us to do. Let me draw some axes over here. And I'll be in the first quadrant since we're dealing with earnings, so neither of their earnings can be negative. And let me just define the vertical axis as Abby's axis or the Abby's earnings axis. And let me define the horizontal axis as Ben's axis or Ben's earnings axis. And let me just graph each of these equations. And to do that, I'm going to take this first equation, and I'm going to put it in the equivalent of slope-intercept form. It might look a little unfamiliar to you, but it really is slope-intercept form. Let me rewrite it first. So we have A plus B is equal to 50. We can subtract B from both sides. So let's subtract B from both sides. And then we get A is equal to negative B plus 50. So if you think about it this way, when B is equal to 0, A is going to be 50. So we know our A intercept, we could call it. We normally would call that a y-intercept, but now this is the A axis. So this right here, let me call this 10, 20, 30, 40, and 50. So if Ben made $0, then Abby would have to make $50 based on that first constraint. So we know that that's a point on the line right over there. And we also know that the slope is negative 1, that B is the independent variable, the way I've written it over here, and this coefficient is negative 1. Or another way to think about it is if A is 0, then B is going to be 50. If Abby made no money, then Ben would have to make $50. And that falls purely out of this equation right here. If Abby made nothing, then Ben would have to make $50, so 10, 20, 30, 40, 50. So those are those two situations and every point in between will satisfy this first constraint. So let me connect the dots. So it would look something like that. That's due to this first constraint, due to the fact that together they earned $50. Now, let's think about the second one. Abby earned $10 more than Ben. So that's this equation right here. And it's really already in our slope-intercept form. If Ben made $0, then Abby would make $10. So that's our A intercept. So it's right over there. We could keep doing that. Our slope is going to be 1 here. If Ben makes $10, then Abby's going to make $20. If Ben makes $20, Abby's going to make $30. We could keep going, but I think this gives us the general direction. It already hints at a point of intersection. So just eyeballing it, so we've graphed to the two constraints, together they earned $50. That's the magenta constraint right over here. Abby earned $10 more than Ben. That's this green constraint right over here. And it looks like we have a point of intersection. And it looks like we have a point of intersection at Ben earning $20. Let me label this as 10, 20, 30, 40, and 50. So this is Ben earning $20 and Abby earning-- this is 10, 20, and 30. And Abby earning $30. So just eyeballing it off of this, it looks like A is 30 and B is 20. And let's go verify, make sure that these levels of earnings for Abby and Ben actually satisfy both constraints. So the first constraint is that Abby plus Ben have to make $50. Well, $30 plus $20 is $50. So it meets our first constraint. The second constraint is that Abby earned $10 more than Ben, that Abby is equal to Ben plus 10. Well, once again, over here, Abby is making $10 more than Ben. So it meets our second constraint. And we only have two of them. So it meets both of them. So that's our solution. Abby earned $30. Ben earned $20.