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
V125BC [204]
3 years ago
12

In Exercises 40-43, for what value(s) of k, if any, will the systems have (a) no solution, (b) a unique solution, and (c) infini

tely many solutions?x - 2y +3z = 2x + y + z = k2x - y + 4z = k^2
Mathematics
1 answer:
svet-max [94.6K]3 years ago
5 0

Answer:

If k = −1 then the system has no solutions.

If k = 2 then the system has infinitely many solutions.

The system cannot have unique solution.

Step-by-step explanation:

We have the following system of equations

x - 2y +3z = 2\\x + y + z = k\\2x - y + 4z = k^2

The augmented matrix is

\left[\begin{array}{cccc}1&-2&3&2\\1&1&1&k\\2&-1&4&k^2\end{array}\right]

The reduction of this matrix to row-echelon form is outlined below.

R_2\rightarrow R_2-R_1

\left[\begin{array}{cccc}1&-2&3&2\\0&3&-2&k-2\\2&-1&4&k^2\end{array}\right]

R_3\rightarrow R_3-2R_1

\left[\begin{array}{cccc}1&-2&3&2\\0&3&-2&k-2\\0&3&-2&k^2-4\end{array}\right]

R_3\rightarrow R_3-R_2

\left[\begin{array}{cccc}1&-2&3&2\\0&3&-2&k-2\\0&0&0&k^2-k-2\end{array}\right]

The last row determines, if there are solutions or not. To be consistent, we must have k such that

k^2-k-2=0

\left(k+1\right)\left(k-2\right)=0\\k=-1,\:k=2

Case k = −1:

\left[\begin{array}{ccc|c}1&-2&3&2\\0&3&-2&-1-2\\0&0&0&(-1)^2-(-1)-2\end{array}\right] \rightarrow \left[\begin{array}{ccc|c}1&-2&3&2\\0&3&-2&-3\\0&0&0&-2\end{array}\right]

If k = −1 then the last equation becomes 0 = −2 which is impossible.Therefore, the system has no solutions.

Case k = 2:

\left[\begin{array}{ccc|c}1&-2&3&2\\0&3&-2&2-2\\0&0&0&(2)^2-(2)-2\end{array}\right] \rightarrow \left[\begin{array}{ccc|c}1&-2&3&2\\0&3&-2&0\\0&0&0&0\end{array}\right]

This gives the infinite many solution.

You might be interested in
290°, rotate the terminal side 20° more in the counterclockwise direction
ikadub [295]
the correct answer is 356 degrees hope that helps :) have a great day i hope u get it right because i don’t know it lol
6 0
3 years ago
16−5a+2a−1=41−a<br> what is a?
krek1111 [17]

Answer:

a=-13

Step-by-step explanation:

16−5a+2a−1=41−a

16-1-41 = 5a-2a-a

-26 = 2a

a= -26/2

a=-13

7 0
3 years ago
The equation 9 y minus 6 x = 36 is written in standard form. What is the first step when writing an equivalent equation which so
enot [183]

Answer:

D. Subtract 9y from both sides of the equation.

Step-by-step explanation:

A. Divide both sides of the equation by 36.

B. Multiply both sides of the equation by 6.

C. Add 9y to both sides of the equation.

D. Subtract 9y from both sides of the equation.

Given:

9y - 6x = 36

To solve for x

Step 1: subtract 9y from both sides

9y - 6x - 9y = 36 - 9y

- 6x = 36 - 9y

Step 2: Divide both sides by -6

- 6x / -6 = (36 - 9y) / - 6

x = (36 - 9y) / - 6

The answer is

x = (36 - 9y) / - 6

8 0
3 years ago
Find a number that is between 8/11 and 0.85(repeating) .
professor190 [17]
The answer is C. If you have any questions then leave a comment. Good luck!
7 0
3 years ago
Micah is preparing for a piano recital. He practices for 50 minutes on Monday and 90 minutes on Wensday
SCORPION-xisa [38]

Answer:

She increased 80% the practise time

Step-by-step explanation:

The question is incomplete, the following is missing:

<em>by how much did she increase the time she practised each day? </em>

From Monday to Wednesday she increased 90 - 50 = 40 minutes  the practise time.

To compute the increment as a percentage use: increment/reference *100

In this case, that is: 40/50*100 = 80%, where 50 minutes is taken as a reference.

6 0
3 years ago
Read 2 more answers
Other questions:
  • Whats the answer of 0.02x0.7
    15·2 answers
  • Greatest common factor for 21 and 40
    12·1 answer
  • The volleyball team and the wrestling team at Weston High School are having a joint car wash today, and they are splitting the r
    6·1 answer
  • Evaluate the expression. If necessary, round to the nearest hundredth. e^In5
    7·1 answer
  • What is the volume of the rectangular prism shown ?
    11·1 answer
  • Question 2 : SQUARE ROOTS
    10·2 answers
  • 10 POINTS<br><br>How do you find the absolute deviation of a data
    7·1 answer
  • Please helppppppppppppppppppppp
    6·2 answers
  • Graph the image of rectangle  after a translation 6 units right and 1 unit down.​
    7·2 answers
  • Find the gradient of the line segment between the points (0,3) and (1,8).
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!