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
ludmilkaskok [199]
3 years ago
7

What is the solution to the following system?

Mathematics
1 answer:
leva [86]3 years ago
7 0

Answer:

(4,3,2)

Step-by-step explanation:

We can solve this via matrices, so the equations given can be written in matrix form as:

\left[\begin{array}{cccc}3&2&1&20\\1&-4&-1&-10\\2&1&2&15\end{array}\right]

Now I will shift rows to make my pivot point (top left) a 1 and so:

\left[\begin{array}{cccc}1&-4&-1&-10\\2&1&2&15\\3&2&1&20\end{array}\right]

Next I will come up with algorithms that can cancel out numbers where R1 means row 1, R2 means row 2 and R3 means row three therefore,

-2R1+R2=R2 , -3R1+R3=R3

\left[\begin{array}{cccc}1&-4&-1&-10\\0&9&4&35\\0&14&4&50\end{array}\right]

\frac{R_2}{9}=R_2


\left[\begin{array}{cccc}1&-4&-1&-10\\0&1&\frac{4}{9}&\frac{35}{9}\\0&14&4&50\end{array}\right]


4R2+R1=R1 , -14R2+R3=R3

\left[\begin{array}{cccc}1&0&\frac{7}{9}&\frac{50}{9}\\0&1&\frac{4}{9}&\frac{35}{9}\\0&0&-\frac{20}{9}&-\frac{40}{9}\end{array}\right]


-\frac{9}{20}R_3=R_3

\left[\begin{array}{cccc}1&0&\frac{7}{9}&\frac{50}{9}\\0&1&\frac{4}{9}&\frac{35}{9}\\0&0&1&2\end{array}\right]


-\frac{4}{9}R_3+R_2=R2 , -\frac{7}{9}R_3+R_1=R_1


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


Therefore the solution to the system of equations are (x,y,z) = (4,3,2)

Note: If answer choices are given, plug them in and see if you get what is "equal to".  Meaning plug in 4 for x, 3 for y and 2 for z in the first equation and you should get 20, second equation -10 and third 15.

You might be interested in
How to slove for extraneous solutions
Snezhnost [94]
The answer is 23 
 HOPED THIS HELPED :)
5 0
3 years ago
Sabrina has designed a rectangular painting that measures 60 feet in length and 40 feet in
Ganezh [65]

Answer:

100

Step-by-step explanation:

5 0
2 years ago
Find each measurement to the nearest tenth use 3.14 for pi. r=_ ; d=_ ; C= 17.8 m
jarptica [38.1K]
C = pi×diameter  OR C = 2pi×radius
So...
17.8 = pi×diameter    17.8 = 2pi×radius
17.8/pi = diameter      17.8/2pi = radius
<span>5.66591597407 = diameter or d
</span><span>2.83295798704 = radius or r</span>
8 0
3 years ago
How many times 9 go into 20
Genrish500 [490]
20:9=\dfrac{20}{9}=\dfrac{18+2}{9}=\dfrac{18}{9}+\dfrac{2}{9}=2\dfrac{2}{9}

Answer: 2 times.
8 0
3 years ago
Find the equation of the line that is perpendicular to -x+2y=11 and passes through the point (6,-5).
Serggg [28]

Step-by-step explanation:

m=-2

y+5=2(x-6)

y+5=2x-12

y=2x-17

6 0
3 years ago
Read 2 more answers
Other questions:
  • Find the local maximum and minimum values and saddle point(s) of the function.
    7·1 answer
  • Find the x-intercepts of the parabola with vertex (-7,45)
    14·1 answer
  • Last year, the tree in Pedro's front yard was 5.6 feet tall. This year, the tree is 2 feet less than the hight of Pedro's house.
    9·2 answers
  • Lisa is asked to draw a triangle with the following specifications:
    11·1 answer
  • A batch of 50 parts contains six defects. If two parts are drawn randomly one at a time without replacement, what is the probabi
    14·1 answer
  • Sam is staining the wooden floor of a court. The court is in the shape of a rectangle. Its length is 33 feet and its width is 32
    7·2 answers
  • Which expression is equivalent to 2x² + 7x + 4?
    8·1 answer
  • What is the value of the expression shown? 4[4.5 − 2(1.2)]
    7·1 answer
  • The regular price for a pair of jeans is $36. the sale price is 45% off the regular price. What is the sale price of jeans?
    5·1 answer
  • Kuvvet bir şeyi olçen şeye kuvvet denir​
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!