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Ad libitum [116K]
3 years ago
12

If two equations are graphed, how can you find the solution to the system of equations?

Mathematics
1 answer:
Pavel [41]3 years ago
7 0

Answer:

If the lines intersect, the System of equations has One Solution.

The point of intersection between the lines is the solution of the System of equations.

Step-by-step explanation:

 By definition, given a System of Linear equations, if the lines intersect its means that that System of equations has One Solution.

 Then, the point of intersection  (x,y)  between the lines is the solution of the System of equations.

Observe the graph attached in the exercise.

You can notice that the are two lines which are intersecting each other at a point.

 In this case, you can identify that the intersection between those lines are at the following point:

(3,3)

Where:

x=3\\\\y=3

(Observe the picture attached)

That is the solution of the System of equations.

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PLEASE HELP!!!!<br> I need to solve for a, b, and c
nirvana33 [79]

Answer:

  • 25000 seats in section A
  • 14100 seats in sectin B
  • 10900 seats in section C

Step-by-step explanation:

The problem statement tells you half the total number of seats are in section A, so you already know that there are 25000 A seats. The revenue from those seats is

... 25000×$25 = $625,000

so the revenue from B and C seats must total

... $1,070,500 - 625,000 = $445,500

If all 25000 of the B/C seats were C seats, the revenue would be

... 25000×$15 = $375,000

The actual revenue from those seats is $445,500 -375,000 = $70,500 more than that. We know each B seat generates $5 more revenue, so there must be ...

... $70,500/$5 = 14,100 . . . . B seats

Then the balance of the 25000 B and C seats are C seats:

... 25,000 - 14,100 = 10,900 . . . . C seats

_____

<em>Alternate Solution Method</em>

The new Brainly answer format requires the answer be supplied before the working. In order to find the answer quickly so that I can fill in that section, I used a matrix method for solving the problem. The problem equations can be written ...

  • a + b + c = 50000
  • a - b - c = 0
  • 25a + 20b + 15c = 1070500

so the augmented matrix is ...

\left[\begin{array}{cccc}1&1&1&50000\\1&-1&-1&0\\25&20&15&1070500\end{array}\right]

A graphing calculator can be used to find the solution to this, generally using a function that produces the reduced row-echelon form. The attachment shows the solution using a TI-84 calculator.

___

<em>Comment on the Working</em>

Since the number of A seats is equal to the total of B and C seats, the number of A seats must be half the total number of stadium seats. Having figured that out, the problem is reduced to one of finding the mix of B and C seats that will produce the remaining revenue.

As with many mixture problems, it is convenient to look at differences. Start with the assumption that all of the desired revenue comes from the least contributor. Here, that is C seats. Then figure the difference that using a B seat makes ($20 -15 = $5) and the difference of the actual revenue and the amount that you got by assuming all C seats: 445,500 -375,000 = 70,500. Since replacing a C seat by a B seat adds $5 to the revenue, it is easy to figure the number of such replacements required in order to raise the revenue by $70,500.

If you write the equation for B seats, you find the solution to the equation mirrors this verbal description:

... 20b + 15(25000-b) = 445,500

... 5b = 445,500 - 375000 . . . . simplify, subtract 375000

... b = 70500/5 = 14100

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Ninety percent of recent car buyers say safety was an important factor in their purchase. Yet of these car buyers, only half con
Tresset [83]

Answer:(E) Anyone to whom safety is an important factor in purchasing a car will consult an objective source of vehicle safety information before buying.

Step-by-step explanation: Safety is a term which means the various steps and Activities and processes taken or put in place in order to prevent hazard or damages to an individual,a group of persons,the environment or properties.

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What is the solution to h + 6 = 11
Alexandra [31]
h = 5
11 - 6 = H
so therefore h = 5
5 0
3 years ago
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