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
barxatty [35]
3 years ago
6

Pre-Calculus - Systems of Equations with 3 Variables please show work/steps

Mathematics
1 answer:
inessss [21]3 years ago
3 0

Answer:

x = 10 , y = -7 , z = 1

Step-by-step explanation:

Solve the following system:

{x - 3 z = 7 | (equation 1)

2 x + y - 2 z = 11 | (equation 2)

-x - 2 y + 9 z = 13 | (equation 3)

Swap equation 1 with equation 2:

{2 x + y - 2 z = 11 | (equation 1)

x + 0 y - 3 z = 7 | (equation 2)

-x - 2 y + 9 z = 13 | (equation 3)

Subtract 1/2 × (equation 1) from equation 2:

{2 x + y - 2 z = 11 | (equation 1)

0 x - y/2 - 2 z = 3/2 | (equation 2)

-x - 2 y + 9 z = 13 | (equation 3)

Multiply equation 2 by 2:

{2 x + y - 2 z = 11 | (equation 1)

0 x - y - 4 z = 3 | (equation 2)

-x - 2 y + 9 z = 13 | (equation 3)

Add 1/2 × (equation 1) to equation 3:

{2 x + y - 2 z = 11 | (equation 1)

0 x - y - 4 z = 3 | (equation 2)

0 x - (3 y)/2 + 8 z = 37/2 | (equation 3)

Multiply equation 3 by 2:

{2 x + y - 2 z = 11 | (equation 1)

0 x - y - 4 z = 3 | (equation 2)

0 x - 3 y + 16 z = 37 | (equation 3)

Swap equation 2 with equation 3:

{2 x + y - 2 z = 11 | (equation 1)

0 x - 3 y + 16 z = 37 | (equation 2)

0 x - y - 4 z = 3 | (equation 3)

Subtract 1/3 × (equation 2) from equation 3:

{2 x + y - 2 z = 11 | (equation 1)

0 x - 3 y + 16 z = 37 | (equation 2)

0 x+0 y - (28 z)/3 = (-28)/3 | (equation 3)

Multiply equation 3 by -3/28:

{2 x + y - 2 z = 11 | (equation 1)

0 x - 3 y + 16 z = 37 | (equation 2)

0 x+0 y+z = 1 | (equation 3)

Subtract 16 × (equation 3) from equation 2:

{2 x + y - 2 z = 11 | (equation 1)

0 x - 3 y+0 z = 21 | (equation 2)

0 x+0 y+z = 1 | (equation 3)

Divide equation 2 by -3:

{2 x + y - 2 z = 11 | (equation 1)

0 x+y+0 z = -7 | (equation 2)

0 x+0 y+z = 1 | (equation 3)

Subtract equation 2 from equation 1:

{2 x + 0 y - 2 z = 18 | (equation 1)

0 x+y+0 z = -7 | (equation 2)

0 x+0 y+z = 1 | (equation 3)

Add 2 × (equation 3) to equation 1:

{2 x+0 y+0 z = 20 | (equation 1)

0 x+y+0 z = -7 | (equation 2)

0 x+0 y+z = 1 | (equation 3)

Divide equation 1 by 2:

{x+0 y+0 z = 10 | (equation 1)

0 x+y+0 z = -7 | (equation 2)

0 x+0 y+z = 1 | (equation 3)

Collect results:

Answer: {x = 10 , y = -7 , z = 1

You might be interested in
(01.04)
Ymorist [56]

Answer:2

Step-by-step explanation: the equation is in linear form y=mx+b, the b represents the y intercept in your equation that would be -5

5 0
3 years ago
Solve for variable y answer in simplest radical form
ASHA 777 [7]

Answer:

option A

Step-by-step explanation:

option A y = 9√3 is the correct answer .

In∆ PQR

cos 30 = y /18

√3/2 = y / 18

y = 9√ 3

plz mark my answer as brainlist plzzzz.

hope this will be helpful to you .

4 0
3 years ago
Is 7 a foctor of 93?<br>Explain your answer using words.​
Sveta_85 [38]

No, because 93/7 is not a rational number

I would really really appreciate it if you marked me as brainiest ☆〜(ゝ。∂)

4 0
3 years ago
Isabella ran a lemonade stall at a school festival. She made a $10 profit in the first hour, a $ 25 loss in the second hour, and
Anni [7]

Answer:

$8 loss

Step-by-step explanation:

$10 profits, $7 profits, $25 loss

$10+$7=$17 profits

$25 loss - $17 profits = $8 loss

4 0
3 years ago
grace rides her bike with a constant speed of 18 km/h how long will she take to travel a distance 72 kilometers
atroni [7]
If she rides her bike 18 km per hour
then it will take 4 hours to travel 72 km (72÷18)
the answer is 4
7 0
4 years ago
Other questions:
  • Help n if so show work :(
    11·2 answers
  • Ben is 121212 years older than Ishaan. Ben and Ishaan first met two years ago. Three years ago, Ben was 444 times as old as Isha
    7·2 answers
  • 784.5, 78.45, 7.845 find the next two numbers
    5·2 answers
  • 2 to the power of negative 2​
    9·2 answers
  • The marked price of an article is 25% above its selling price and the cost price is 30% less than its marked price . find the di
    12·1 answer
  • 3x - y = 2<br>and<br>2x + y = 4​
    10·1 answer
  • How can you decompose the composite figure to determine its area?
    11·2 answers
  • Find the volume of the sphere. Use 3.14 for π. Round to the nearest tenth.
    11·1 answer
  • I need help with solving this equation
    6·1 answer
  • 3. Which represents the problem below?
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!