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
Mashutka [201]
3 years ago
11

For which values of k does the system of linear equations have zero, one, or an infinite number of solutions? [Note: not all thr

ee possibilities need occur.] (If the answer is an interval of numbers, enter your answer using interval notation. If an answer does not exist, enter DNE.) 3x1 − x2 = 2 9x1 − 3x2 = k
Mathematics
1 answer:
viktelen [127]3 years ago
4 0

Answer:

The system has an infinite solution at k = 6, otherwise for any value of k, it has zero solution.

Step-by-step explanation:

Consider the system of linear equations:

3x_{1} -x_{2}=2\;\;\;\;\;\;(1)\\ 9x_{1} -3x_{2}=k\;\;\;\;\;(2)

The system of linear equations can have zero, one, or an infinite number of solutions:

simplify equation (1):

x_{2}=3x_{1} -2

substitute in equation (2), we get

9x_{1} -3(3x_{1}-2)=k\\9x_{1} -9x_{1}+6=k\\0+6=k

we cannot find the value of x_{1} and x_{2}.

so, there is no solution.

Multiply the equation (1) with 3 and put k is 6,

3(3x_{1} -x_{2})=3\times2\\9x_{1} -3x_{2})=6

it means both equations are overlapped. Then, the solution has infinite solutions.

Hence, the system has an infinite solutions at k is 6 otherwise for any value of k it has no solution.

You might be interested in
What is $60times 1/5
RoseWind [281]
It should be 12 because 60/5 =12

5 0
3 years ago
2-tert-butyl-3-methylhexane​
kumpel [21]

Answer:

Please upload this question properly

3 0
3 years ago
Which expression below is equivelent to (9x-4) 13(3x-2)?
siniylev [52]
Can you give me the expressions?
5 0
3 years ago
Please help ASAP!!! Tysm :)
Sveta_85 [38]

Answer:

Hope that will help you

Step-by-step explanation:

BD = 14.5

3 0
3 years ago
Name the type of transformation that maps the pre-image, ABC, to the image, A'B'C'. show your work​
AleksAgata [21]

Answer:

reflection across y translate 1 unit to the right translate 6 units down

Step-by-step explanation:

6 0
3 years ago
Other questions:
  • What is a improper faction
    11·2 answers
  • If a person with a height of 58 inches takes 2,601 steps per mile, a person with a height of 64 inches takes 2,357 steps per mil
    6·1 answer
  • Given the functions m(x) = 4x − 11 and n(x) = x − 10, solve m[n(x)]
    5·1 answer
  • What is 2/3+1/4 please answer immediately
    6·2 answers
  • Which angles are complementary to each other ? select all that apply
    10·2 answers
  • PLEASE I REALLY NEED HELP AND PLEASE PLEASE NO LINKS!!
    15·1 answer
  • If bob had 4 apples and tim had 6 oranges but john had 4 times more oranges then tim but stephaine had 6 times more apples then
    11·1 answer
  • Stack of wood 4 feet wide 8 feet long and 4 feet high is equal to 1 quart of wood. How many quarts would a pie 4 feet wide and 1
    15·1 answer
  • How to turn a fraction to a decimal
    13·1 answer
  • Im going to give brainly plz help me thx i promise.
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!