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
kolbaska11 [484]
2 years ago
14

Determine which system below will produce infinitely many solutions.

Mathematics
1 answer:
DaniilM [7]2 years ago
4 0
<span>A.  −6x + 3y = 18 4x − 3y = 6
B   2x + 4y = 24 6x + 12y = 36
C.  3x − y = 14 −9x + 3y = −42
D.  5x + 2y = 13 −x + 4y = −6

For infinitely many solutions,  we are looking for linearly dependent equations, which means that one equation is an exact multiple or sub-multiple of the other.
Example: 
</span>2x + 4y = 24
6x + 12y = 36
<span>is a system that does NOT have a solution, because 6/2=3 for x, 12/4=3 for y, but 36/24=1.5.  The two lines have the same slope (therefore parallel), but they have different y-intercepts.  So the two lines will never meet, and therefore no solution.


or another example:
</span>  3x  -y = 14
  -9x + 3y = -42
We see that -9/3=-3, 3/-1=-3, -42/3=-14, this system has coefficients all in the same ratio, meaning that the lines are coincident (and linearly dependent), therefore infinitely many solutions.

Still another example:
−6x + 3y = 18
4x − 3y = 6
we see that 18/6=3, 3/(-3)=-1 , since the ratios are different, the two equations are not linearly dependent, and therefore the system has unique solution.

Last example:
5x + 2y = 13
−x + 4y = −6
Check the ratio of the coefficients:
-1/5=-1/5
4/2=2  ..... we can stop here and conclude that there is a unique solution because the equations are not in the same ratio. (unique means that there is exactly one solution)

You might be interested in
77 kL ____ 77mL <br><br> Is it <br> &lt;<br> &gt;<br> =
sasho [114]

Answer:

>

Step-by-step explanation:

The ratio of kL to mL is 1,000,000. So 77 kL is equal to about 77,000,000 mL. Meaning 77 kL > 77 mL.

7 0
3 years ago
Read 2 more answers
I NEED HELP WITH THIS PLEASEEE
Alexxx [7]

Answer:

The probability of it being greater than 6 is 3/4.

Step-by-step explanation:

there are 4 outcomes, and 6 is only one of them. 3 are greater than 6, so 4 out of the 4 times the number will be greater than 6.

7 0
3 years ago
Read 2 more answers
Find the missing value of a triangle one leg is 12 and the long side is 20 what is the other leg?
Burka [1]
Simple,

using the Pythagorean Theorem...

a^{2} + b^{2} = c^{2}

You have the hypotenuse (C) and one of the legs (A)

So, plug in what you know...

12^{2}+ b^{2}  = 20^{2}

144+b^{2}=400

Now,isolate b^{2}

144+ b^{2} =400
-144                   -144

Leaving you with...

b^{2} =256

So, now, \sqrt{256}, to find what b is..

b=16

Thus, your answer.
3 0
3 years ago
Read 2 more answers
Please awnser questions, no links, no I dont know 2.
uysha [10]
3 boxes of 12″ =36 = 2 boxes of 18″

so shortest height at which the 2 stack will be the same height =36 inches
4 0
3 years ago
If points N, U, and T are collinear, name all the segments they determine.
nexus9112 [7]
Collinear=On the same line

N-U

N-T

U-T

I believe that is what this questions is asking. :)
3 0
3 years ago
Read 2 more answers
Other questions:
  • The factory owner asks Ella to design a new box. The box is a rectangular prism. Ella’s design is shown below.
    8·1 answer
  • What times what can equal 26
    9·2 answers
  • Anyone????????????????
    9·1 answer
  • A monkey is swinging from the tree. On the first swing she passes through an arc of 20 m. With each swing she passes through an
    15·2 answers
  • A spinner is divided into four equal sections labeled 1, 2, 3, and 4. Another spinner is divided into three equal sections label
    9·2 answers
  • Please help me all if this or anything you can do thank you
    15·1 answer
  • The ratio of the side lengths of two squares is 2:5. What is the ratio of the areas of the same two squares?
    7·1 answer
  • On which number line do the points represent negative 4 and 1 over 2 and +3? (4 points)
    13·2 answers
  • What is the distance between Point A and Point B ?
    14·1 answer
  • Using a loan calculator, find the total cost to repay a three month long credit card loan with a principal of $480 and an intere
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!