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
diamong [38]
3 years ago
5

A first number plus twice a second number is 1. Twice the first number plus the second totals 14. Find the numbers

Mathematics
2 answers:
Vikentia [17]3 years ago
7 0

Hey there!!

Let's take the first number as ' x '

Let's take the second number as ' y '

First number + twice the second number is 1

x + 2y = 1 ------------ ( 1 )

Twice the second number + second number is 14.

2x + y = 14 ----------- ( 2 )

Now let's get them all together...

...................................................................................................................................................................

x + 2y = 1 --- ( 1 )

2x + y = 14 --- ( 2 )

Now, let's multiply the first equation with 2 ...

...................................................................................................................................................................

2x + 4y = 2 --- ( 1 )

2x + y = 14 --- ( 2 )

Now, let's subtract the second equation from the second...

...................................................................................................................................................................

2x + 4y = 2 --- ( 1 )

- ( 2x + y ) = - ( 14 )

...................................................................................................................................................................

2x + 4y = 2 --- ( 1 )

-2x - y = -14 --- ( 2 )

...................................................................................................................................................................

3y = -12

Divide by 3 on both sides...

y = -4

The second number is -4.

We have the first equation x + 2y = 1

We got the y value, now substitute the value of y to get the value of x

...................................................................................................................................................................

x + 2y = 1

x + 2 ( -4 ) = 1

x - 8 = 1

Add 8 on both sides

x = 9

Hence, the second number is 9.

...................................................................................................................................................................

Hope my answer helps!!


poizon [28]3 years ago
3 0

Let's consider the first number to be f and the second number to be s. Based on the information in the problem, we can create the following equations:

f + 2s = 1

2f + s = 14


Now, we can solve the equations through systems of equations. One way of doing this is by multiplying one of the equations so that there is a term in both equations which can be removed by addition or subtraction. In our case, we can multiply the entire first equation by 2 to get:

2f + 4s = 2/tex][tex]2f + s = 14


Now, subtract 2f from both equations to get:

3s = -12

s = -4


Now that we have found s, "plug" it back into an equation to find f:

f + 2(-4) = 1

f - 8 = 1

f = 9


Our answers are s = -4 and f = 9.

You might be interested in
Lupe and her friends spend $20 on hot dogs and popcorn at a
vodomira [7]

Answer:

They buy 6 hotdogs and 5 popcorn

Step-by-step explanation:

Assume that they buy x hotdogs and y popcorn

∵ They buy a total of 11 hotdogs and popcorn

∵ The number of hotdogs is x and the number of popcorn is y

∴ x + y = 11 ⇒ (1)

∵ Hot dogs cost $2.50 each

∵ Popcorn costs $1.00 each

∵ They spend $20 on hot dogs and popcorn

→ Multiply x by 2.5 and y by 1, add the products and equate the sum by 20

∴ 2.5(x) + 1(y) = 20

∴ 2.5x + y = 20 ⇒ (2)

Now we have a system of equations to solve it

→ Subtract equation (1) from equation (2)

∵ (2.5x - x) + (y - y) = (20 - 11)

∴ 1.5x + 0 = 9

∴ 1.5x = 9

→ Divide both sides by 1.5 to find x

∴ x = 6

→ Substitute the value of x in equation (1) to find y

∵ 6 + y = 11

→ Subtract 6 from both sides

∴ 6 - 6 + y = 11 - 6

∴ y = 5

∴ They buy 6 hotdogs and 5 popcorn

8 0
3 years ago
A family buys 4 airline tickets online. The family buys travel insurance that costs $19 per ticket. The total cost is $752. Let
Ede4ka [16]

A. x = 752 / 4 - 19

B. 169

7 0
3 years ago
Read 2 more answers
5 is 20 percent of what
miskamm [114]

Answer:25 is the answer

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Can anyone help with words problems for algebra 1?
Helga [31]

37.)

68-39= 29˙

38.)

29028-282= 28746 ft

3 0
3 years ago
A club with 31 members is to select five officers (president, vice president, secretary, treasurer, and historian). In how many
Ksivusya [100]
If you take 31*5 that equals = 155 ways! <span />
5 0
3 years ago
Other questions:
  • (6,2),(9,r),m=-1 find the value of r
    13·1 answer
  • Which of these is an example of discrete data?
    15·2 answers
  • 15x - 10 = -9x + 2 <br> please help me !!!!!
    15·1 answer
  • The points (1,7) and (0,5) fall on a particular line. What is its equation in slope-intercept
    11·1 answer
  • Five friends attend a matinee movie and spend $8 per ticket. They also purchase a small bag of popcorn each. If the friends spen
    10·2 answers
  • 11. f(x) = x + 3, g(x) = -x + 2. Find (f + g)(x)
    6·1 answer
  • Based on thr box plot below, which statement is not true?​
    6·1 answer
  • Lin Ying belongs to an athletic club. In 800 m races her times are normally distributed with mean 128 seconds and standard devia
    11·2 answers
  • Find the approximate radius of a circle with a circumference of 198 centimeters. Use 3.14 for it. Round to the nearest
    6·1 answer
  • PLS HELPPPPPP i dont know how to do question 17,18,24
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!