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### Course: College Algebra>Unit 1

Lesson 2: Solutions to linear equations

# Interpreting points in context of graphs of systems

Given a graph of a system of equations and a context, practice interpreting what various points represent in that system.

## Want to join the conversation?

• i hate word problems
• exactly ,moi aussi
• I think I am slowly understanding what this means, however, I feel like I need more practice with it all of it. Also, wherever the variable is on the graph, the number underneath or nearby represents that.
• Simply, Lauren has a sum of money. So she wants to spend this "sum of money" on things like "something." Now the data given about Lauren's situation through Sal's example — we are going to interpret them informally like:

Lauren's sum of money → \$ = \$220
something → beans = 80 kg

Just remember that we have a couple of constraints that intersect at a given point on the graph. They can be given a description at any point on the graph by Khan Academy even when either of conditions: have no intersection, have intersection.
Now, we as mathematicians trying to understand Lauren's problem to solve it, we found out that the problem is a bit complicated, but we are not afraid since mathematics supports us with its tools like variables and constants. That; however, is, it is true that Lauren wants to buy a 80 kg of beans, and, it is false that the beans out there in the market found in a single sort of mass. It is, again, true that the constituents here are two different ones in sort, but Lauren does not matter the equality of one sort, say x, over the other one sort, say y. What does matter for Lauren when buying the beans is the the couple of constituents, which are dark beans + light beans, has both to be equal to 80 kg in total amount. Again, she does not matter about the amount of dark beans to be equal or less to or more than the amount of light beans, and, it can apply to light beans in reverse too. We are going to see how this no-matter-of-equality relationship relates when we expand on the analysis of data given to Lauren's problem.

If we go back to the context of the problem, we'd see clearly that the price of the dark beans (\$3) is higher in one degree than the price of light beans (\$2). So it's obvious to learn that Lauren is going to get more light beans than dark beans in kilograms! Again, we as mathematicians have to clear concise to the problem we are stated, which means Lauren's is neither interested in a relation of knowing which constituent x is less than or equal to constituent y, nor are we interested in a relation of knowing which constituent y is more than or equal to constituent x. We mathematicians use less words! We say that Lauren is not interested in a relation of an inequality equation to x and y, like for instance, x ≤ y or x ≥ y, but we are interested in beyond! What's interesting for Lauren's and we is we have constraints: a: 3(60)+ 2(20) = 220, b: 20 + 60 = 80. This what means to have constraints. Remember that the constraints given we need them to be met like 0 = 0. If not, for example, a: 3(10) + 2(96) = 220, b: 10 + 96 = 80, then we are going to use descriptions in language instead to show such a relation of a fact deviation.

Now let's go deep into Lauren's problem. The constraints given are a and b. a represents the sum of money in \$, b represents the amount of beans in kg. So far so good. Remember that both constraints have to intercept at the same point of (x, y) on the graph to have the a condition 3x + 2y = 220 to be exactly like a: 3(60) + 2(20) = 220 :: 220 = 220, and the b condition x + y = 80 :: 60 + 20 = 80 to be exactly like 80 = 80. *If both constraints don't meet at the same point, this means that *each constraint would have a point of (x, y) on the graph, like: a: (x2, y2), and b: (x2, y2).*

Now let's pick each point on the graph and see how it looks like:

Point *C
shows at a point of *(10, 95)* for the a constraint, and the b constraint down right below C shows at point of (10, 70), we get:

point C of (10, 95)*

a: 3x + 2y = 220
3(10) + 2(95) = 220
220 = 220

b: x + y = 80
10 + 95 = 80
105 = 80

This is if *a
and b were to intersect at (10, 95) whereas only a does, and, even though they do intersection at that point the system of equation would dissolve from the side of constraint b.*

point down right below C (10, 70)

a: 3x + 2y = 220
3(10) + 2(70) = 220
30 + 140 = 220
170 = 220

b: x + y = 80
10 + 70 = 80
80 = 80

This is if *a
and b were to intersect at (10, 70) whereas only b does, and, even though they do intersection at that point the system of our equation would dissolve from the side of constraint a.

So what we can see is a and b as two constraints fail to intersect at point C of (10, 95)* to satisfy the system of our equation. In description, we would say about point C that, *Lauren spends the intended amount of money and buys more than the intended amount of beans.* The point *down right below C at (10, 70)* also fails like the one above it that C, which we would describe it like "Lauren spends less than the intended amount of money and buys the same intended amount of beans.*

Let's continue with other the points of *D, F, and E
and their descriptions: (Notice that I am using the same descriptive language by Khan Academy)

point D of (20, 60)

a: 3x + 2y = 220
3(20) + 2(60) = 220
60 + 120 = 220
180 = 220

b: x + y = 80
20 + 60 = 80
80 = 80

Description
Lauren spends less than the intended amount of money and buys the same intended amount of beans.*

point F of (30, 30)

a: 3x + 2y = 220
3(30) + 2(30) = 220
90 + 60 = 220
150 = 220

b: x + y = 80
30 + 30 = 80
60 = 80

*Description

Lauren spends less than the intended amount of money and buys less than the intended amount of beans.*

point E of (60, 20)

a: 3x + 2y = 220
3(60) + 2(20) = 220
180 + 40 = 220
220 = 220

b: x + y = 80
60 + 20 = 80
80 = 80

*Description

Lauren spends the same intended amount of money and buys the same intended amount of beans.*

Finally, We can see how *the point E of (60, 20),* that by which both constraints of *a
and b are intersected.
• what is this i dont get it
• man im poor in points
• if you rewind the video to a few seconds before it ends and watch those few seconds over and over its an infinite point glitch!
• I think I am slowly understanding what this means, however, I feel like I need more practice with it all of it. Also, wherever the variable is on the graph, the number underneath or nearby represents that.
• You can do it! Practice until you can't get it wrong :)
(1 vote)
• What does dark and light represent?, so confusing
• dark=dark roast and light=light roast
(1 vote)
• Yo I respect the people who took the time to make and edit this video and so many more.