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
BARSIC [14]
3 years ago
9

If the second number is subtracted from the sum of the first number and 2 times the third number, the result is 1. The thrid num

ber plus 2 times the first number is 3. The first number plus 3 times the second number plus the third number is 18. Find the three numbers.
Mathematics
1 answer:
weeeeeb [17]3 years ago
7 0

Answer:

<h2>x = 0, y = 5, z = 3</h2>

Step-by-step explanation:

x,\ y,\ z-\text{three numbers}\\\\\left\{\begin{array}{ccc}(x+2z)-y=1&(1)\\z+2x=3&(2)\\x+3y+z=18&(3)\end{array}\right\\\\(2)\\z+2x=3\qquad\text{subtract}\ 2x\ \text{from both sides}\\z=3-2x\qquad(*)\\\\\text{Substitute}\ (*)\ \text{to (1) and (3)}\\\\\left\{\begin{array}{ccc}x+2(3-2x)-y=1&\text{use the distributive property}\\x+3y+(3-2x)=18\end{array}\right

\left\{\begin{array}{ccc}x+(2)(3)+(2)(-2x)-y=1\\x+3y+3-2x=18&\text{subtract 3 from both sides}\end{array}\right\\\left\{\begin{array}{ccc}x+6-4x-y=1&\text{subtract 6 from both sides}\\(x-2x)+3y=15\end{array}\right\\\left\{\begin{array}{ccc}(x-4x)-y=-5\\-x+3y=15\end{array}\right\\\left\{\begin{array}{ccc}-3x-y=-5&\text{multiply both sides by 3}\\-x+3y=15\end{array}\right

\underline{+\left\{\begin{array}{ccc}-9x-3y=-15\\-x+3y=15\end{array}\right}\qquad\text{add all sides of the equations}\\.\qquad-10x=0\qquad\text{divide both sides by (-10)}\\.\qquad\boxed{x=0}\\\\\text{Put it to the second equation:}\\-0+3y=15\\3y=15\qquad\text{divide both sides by 3}\\\boxed{y=5}\\\\\text{Put the value of}\ x\ \text{to}\ (*):\\\\z=3-2(0)\\\boxed{z=3}

You might be interested in
The cost of a pizza is $8.50 plus $1.35 per topping. How many toppings are on a pizza that costs $13.90?
VMariaS [17]

Answer:  

8.50 + 1.35n = 13.90

Step-by-step explanation:

So basically you have to add the cost of pizza and the per toppings correct me if i'm wrong Also Have a good Wonderful day!

And that's 4 toppings

3 0
3 years ago
Read 2 more answers
A restaurant had 82.4 pounds of meat, then they ate 5.5 pounds of it, how much is left
zheka24 [161]

Answer:76.9 pounds

Step-by-step explanation: you subtract 5.5 pounds from the 82.4 pounds to get your answer

5 0
2 years ago
Read 2 more answers
Write an EQUATION for the nth term of each arithmetic sequence<br><br> -1,-0.5,0,0.5,...
kaheart [24]
Ninth term is 2.5

you are adding 0.5 each time

-1,-0.5,0,0.5,1,1.5,2,2.5
8 0
3 years ago
One way to compute a 20% tip for a bill is to multiply it by 0.20. A restaurant bill was $35.70. Calculate the tip.
Dafna1 [17]

Answer:

7.14

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
A cheetah's speed was timed over a set distance. The cheetah was clocked running 60 miles per hour. Which equation is the relati
Troyanec [42]

Answer:

D. y=70x

Step-by-step explanation:

The cheetah was clocked running 70 miles per hour.

i.e. in 1 hour cheetah covered 70 miles

in 2 hours cheetah covered 140 miles

in 3 hours cheetah covered 210 miles

in general, in n hour cheetah covered 70n miles

If y denote the distance covered

and x denotes the time cheetah runs

Then, y=70x

Hence, the equation which shows the relationship between the distance, y, and time, x, the cheetah runs is:

D  y=70x

8 0
3 years ago
Other questions:
  • Help me with 234 thousands + 7 ten thousands = need answer ASAP!<br><br> Thanks
    14·2 answers
  • I neeeedddd help with this question
    14·2 answers
  • Solve for c: 6/15=2/c
    10·1 answer
  • marco has a piece of wood that measures 9 x 1/10 6 x 1/100 4 x 1/1000 meter. how can this measurement be written as a decimal?
    13·1 answer
  • Which expression represents a number that is one fourth as great as 10-2?
    11·1 answer
  • A sequence has the recursive rule f(n)=2f(n-1). The first term of the sequence is 7. Write the first 3 terms of the sequence
    8·1 answer
  • Two trains left the cities A and B at the same time and headed towards each other. The cities are s miles apart. The first train
    12·1 answer
  • Sally plans to enclose a square garden with fencing. The area of the garden is 1600 square feet. How many feet of fencing does s
    14·2 answers
  • What is the measure of angle 5 ?​
    7·1 answer
  • What is 48 divided by 1.35
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!