1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
spin [16.1K]
3 years ago
7

Determine if the solution set for the system of equations shown is the empty set, contains one point or is infinite. x + y = 6 x

- y = 0
Mathematics
1 answer:
zhuklara [117]3 years ago
5 0
Answer:  [B]:  "contains one point" .
_______________________________
Explanation:
__________________
Given:
__________________
x + y  = 6  ;
x - y = 0 ;
_________________
 
To solve for "x" ;

Consider the first equation:

x + y = 6 ;

subtract "y" from each side of the equation ; to isolate "x" on one side of the equation; and to solve for "x" ;

x + y - y = 6 - y ;

x = 6 - y ;
________________
Take the second equation:
____________________
 x - y = 0 ;

Solve for "x" ;

Add "y" to EACH SIDE of the equation; to isolate "x" on one side of the equation; and to solve for "x" ;

x - y + y = 0 + y ;
________________________________
    x = y
______________
x = 6 - y

Substitute "x" for "y" ;

x = 6 - x ;

Add "x" to Each side of the equation:
_______________________________
x + x = 6 - x + x ;

2x = 6 ;

Now, divide EACH SIDE of the equation by "2" ; to isolate "x" on one side of the equation; and to solve for "x" ;

2x/2 = 6/2 ;

x = 3 .
_______________
Now, since "x = 3" ;  substitute "3" for "x" in both original equations; to see if we get the same value for "y" ;
_______________________________
x + y  = 6  ;
x - y = 0
________________________________
Start with the first equation:
________________________________
x + y = 6 ;

3 + y = 6 ;

Subtract  "3" from each side of the equation; to isolate "y" on one side of the equation; and to solve for "y" ;

3 + y - 3 = 6 - 3 ;

y = 3 .
________________________
Now, continue with the second equation; {Substitute "3" for "x" to see the value we get for "y"} ;
________________________
The second equation given is:
________________________
x - y = 0 ;

Substitute "3" for "x" to solve for "y" ;

3 - y = 0 ;

Subtract "3" from EACH side of the equation:

3 - y - 3 = 0 - 3 ;

      -1y = -3  ;

Divide EACH side of the equation by "-1" ;  to isolate "y" on one side of the equation; and to solve for "y" ;

-1y/-1 = -3/-1 ;

    y = 3 .
________________________
So, for both equations, we have one value:  x = 3, y = 3;  or:  write as: 
"(3, 3)" ;  { which is:  "one single point" ;  which is:  Answer choice:  [B] } .
__________________________________________________________ 
You might be interested in
The stem plot shows the number of swimming laps completed by swim team members at a single practice.
Juliette [100K]

The question is incomplete. Here is the complete question.

The stem plot shows the number of swimming laps completed by the swim team members at a single practice.

5       7 9

6       1 2 3 4

7       6 6

8

9

10

11

12      5

What is a correct statement about distribution?

There no outliers

The distribution is symmetric

The center is around 80

The distribution is unimodal

The spread is from 57 to 89.

Answer: The distribution is unimodal.

Step-by-step explanation: <u>Stem</u> <u>Plot</u> is an unique way of writing numbers in a table. Each value is split into a "stem" (first digit or digits) and a "leaf" (usually the last digit).

For the swim team practice, we have:

57, 59, 61, 62, 63, 64, 76, 76, 125

Note that, although there the digits 8, 9, 10, and 11, there no "leaves" for them, so, the values are not part of the distribution.

<u>Outlier</u> is a value that lies outside most of other values. In the distribution there is the value 125 which is very much more than other values, i.e., it is an outlier, so, alternative "There no outliers" is false;

Ploting the values on a frequency graph, it shows a curve skewed to the right, i.e., deslocated to the right, then, it is not symmetric. Second alternative is false.

The center of the distribution is the middle value, which is 63, then, third statement is false.

The spread of this distribution is from 57 to 125, so fifth statement is incorrect.

An <u>unimodal</u> <u>distribution</u> is a distribution which has only one clear peak or most frequent value. At the swim team distribution, the value that appears more than once is 76, so the peak is at that value. The other values appears just once, so distribution has only one peak. Fourth statement is correct.

8 0
3 years ago
Meg has saved up $350 to purchase a new TV from the local store. The sales tax in her county is 5% of the sticker price. Write a
Sergio [31]

For this case we have:

Let p be the highest price of the TV that Meg can buy

We have to:

5% of p is given by:

0.05p

So, we have:

p + 0.05p = 350

Clearing p we have:

1.05p = 350

p=\frac{350}{1.05}\\p=333.33

Thus, the highest price of the television that Meg purchases should be p = 333.33dollars.

Answer:

p + 0.05p = 350\\p = 333.33


3 0
3 years ago
A 20-foot flagpole casts a 6-foot Shadow how tall is a nearby building that casts a 30-foot shadow
Viefleur [7K]

The building would be 100ft tall. You have to take 20/6 = ?/30 The difference between 6 and 30 is x5. Then all you have to do is 20x5 and you get 100ft.

8 0
3 years ago
Read 2 more answers
You have just started a colony on Mars. One of the biggest concerns for the colony is government. What is your colony going to d
777dan777 [17]

Answer:

we will use democracy so that everyone gets a say in what happens to the colony, second the government will make the decisions and the people will provide options and different ideas, and i believe its the best type because everyone has a say in what happens and the government isn't too powerful and has as much power as the people do.

Step-by-step explanation:

3 0
2 years ago
Here is a rectangle ABCD. The length of the rectangle is increased by 10%. The width of the rectangle is increased by 5%. Find t
sladkih [1.3K]

Answer: Width would become 21 and length would become 33. Original perimeter is 100, increased perimeter is 108 which is a 7.69% increase

6 0
2 years ago
Other questions:
  • In 2002, the population of a district was 22,800. With a continuous annual growth rate of approximately 5% what will the populat
    14·1 answer
  • What is the slope of the line on the graph?
    15·1 answer
  • Four electronic ovens that were dropped during shipment are inspected and classifi ed as containing either a major, a minor, or
    9·1 answer
  • What is the derivative of arctan (y/x) with respect to y??
    7·1 answer
  • What could be used to evaluate the expression -6(4(2/3)
    8·1 answer
  • The sum of the two numbers is 12, and their product is -28.
    7·1 answer
  • Abigail is 5 years older than Brenda.
    10·1 answer
  • Solve for x. Assume that lines which appear tangent are tangent.
    6·1 answer
  • The lengths of text messages are normally distributed with a population standard deviation of 4 characters and an unknown popula
    10·1 answer
  • What additional information would prove that lmnp is a rectangle? the length of lm is startroot 45 endroot and the length of mn
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!