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
ch4aika [34]
3 years ago
15

Solve the system by substitution.

Mathematics
1 answer:
Butoxors [25]3 years ago
4 0

<u>Answer:</u>

The solution set of given equations -x-y-z = -8 and - 4x + 4y + 5z = 7 and 2x + 2z = 4  is (3, 6, -1)

<u>Solution:</u>

Given, set linear equations are

-x – y – z = -8 ⇒ x + y + z = 8 → (1)

-4x + 4y + 5z = 7 ⇒ 4x – 4y – 5z = -7 → (2)

2x + 2z = 4 ⇒ x + z = 2 → (3)

We have to solve the above given equations using substitution method.

Now take (3), x + z = 2 ⇒ x = 2 – z  

So substitute x value in (1)  

(1) ⇒ (2 – z) + y + z = 8 ⇒ 2 + y + z – z = 8 ⇒ y + 0 = 8 – 2 ⇒ y = 6.

Now substitute x and y values in (2)

(2) ⇒ 4(2 – z) – 4(6) – 5z = - 7 ⇒ 8 – 4z – 24 – 5z = -7 ⇒ -9z – 16 = -7 ⇒ 9z = 7 – 16 ⇒ 9z = -9 ⇒ z = -1

Now substitute z value in (3)

(3) ⇒ x – 1 = 2 ⇒ x = 2 + 1 ⇒ x = 3

Hence, the solution set of given equations is (3, 6, -1).

You might be interested in
If EF bisects CD, CG =5x-1, GD = 7x-13, EF = 6x-4, and GF =13, find EG
VARVARA [1.3K]

<em>Greetings from Brasil....</em>

As stated in the statement of the question, EF is a bisector of CD, so point G is the median point of CD, so CG = GD

5X - 1 = 7X - 13

X = 6

EF = EG + GF

6X - 4 = EG + 13      x = 6, so

6·6 - 4 = EG + 13

<h2>EG = 19</h2>

<em>(see attachment)</em>

6 0
3 years ago
A standard die is rolled 360 times in hopes of rolling a 5 or 6. So the probability of success is p=1/3. Find the standard devia
lana [24]

Answer: option 1 is the correct answer

Step-by-step explanation:

Number of times for which the die was rolled is 360. It means that our sample size, n is 360.

The probability of rolling a 5 or a 6 is 1/3. It means that probability of success,p = 1/3. The probability of failure,q is

1 - probability of success. It becomes

1 - 1/3 = 2/3

The formula for standard deviation is expressed as

√npq. Therefore

Standard deviation = √360 × 1/3 × 2/3

= √80 = 8.9443

Standard deviation is approximately 8.9

4 0
3 years ago
PLEASE HELP!!!!!!!!! Solve the system using elimination method.
NeX [460]

Answer:

The answer is (6,12)

107x= 642

x=6

7•6 +2y=66

y= 12

8 0
3 years ago
)
Leto [7]

Answer:

Number of Adult's tickets sold on Saturday = 3,356

Number of Children's tickets sold on Saturday = 2, 928

Total number of tickets sold over these two days is 8,938.

Step-by-step explanation:

Here, the number of tickets sold on FRIDAY:

Adult Ticket sold = 1,678

Children's Tickets sold = 976

So, the total number of tickets sold on Friday  

= Sum of ( Adult + Children's ) tickets  = 1,678  + 976 = 2,654 ....  (1)

The number of tickets sold on SATURDAY:

Adult Ticket sold =   2 times  the number of adult tickets sold on Friday

                            =  1,678 x 2  = 3,356

Children's Tickets sold = 3 times the number of children's tickets sold on Friday.

=  976  x 3 = 2, 928

So, the total number of tickets sold on Saturday  

= Sum of ( Adult + Children's ) tickets  = 3,356 + 2,928 = 6, 284 ....  (2)

Now, the total number of tickets booked in these two days :

Sum of tickets booked on (Friday + Saturday)

= 2,654 +  6, 284  =   8,938

Hence, total number of tickets sold over these two days is 8,938.

6 0
3 years ago
Solve for x<br> (2x - 3)(x - 2) = 0
Zinaida [17]

Answer:

?

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
Other questions:
  • Graph y=3x on the coordinate plane. Identify the unit rate from the graph.
    13·2 answers
  • Carl Can ride his bike twice as fast as he can jog. He jogged three times around a 1 mile trail in 24 minutes and then rode the
    10·2 answers
  • the area of a rectangular floor is 135meter square where one side is 1.5 meter calculate the dimension of the floor
    8·1 answer
  • James thinks the perimeter of this figure is 6x + 10. Ana thinks it is 6x + 6. Who is
    12·1 answer
  • Question 12<br>mº<br>680<br>80° 60 750<br>Find the value of mº in the diagram below​
    6·1 answer
  • A rectangular field has an area of 2100 square feet. the length of the field is 50 feet.
    11·1 answer
  • A volleyball team won 90% of 80 games played.how many games did they win?
    15·1 answer
  • What does an adverb describe? *
    6·2 answers
  • The initial amount of money that is deposited into an account or that is borrowed is called what
    6·2 answers
  • How do you graph an equation using x and y intercepts.
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!