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3 years ago

A collection of animals including both birds and beasts has 43 heads and 120 feet how many based are there in the collection

Mathematics

1 answer:

DaniilM [7]3 years ago

8 0

Step-by-step explanation:

x = number of birds

y = number of beasts

x + y = 43 (as each of these creatures had only 1 head).

2x + 4y = 120 (birds have 2 feet, beasts 4 feet).

x + 2y = 60 (divided both sides by 2)

so, second equation minus the first equation is

(x-x) + (2y-y) = 60-43

y = 17

x + y = 43

x + 17 = 43

x = 26

so, there are 17 beasts and 26 birds.

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What are the methods of substitution?

anyanavicka [17]

Answer:

-One Equation: is set equal to a variable

Example:

y = 2x + 1

x + 3y = -12

You already have y, plug it back into x + 3y = -12

x + 3(2x + 1) = -12

x + 6x + 3 = -12

7x + 3 = -12

(Subtract 3 from each side)

7x = -15

(Divide by 7)

x = - 2.14

-No Equation: is set equal to a variable

Example:

2x + y = 10

4× + 2y = -3

Subtract 2x from each side of 2x + y = 10, you should get y= -2x + 10. Now that you have found y, substitute y into 4x+ 2y = -3.

4x + 2(-2x + 10) = -3

4x + -4x + 20 = -3

(Subtract 20 from each side)

4x + -4x = -23

(Add 4x and -4x)

0 = -23

No Solution

-Both Equations: are set equal to a variable

Example:

y = x + 5

y = -x + 3

(you already have y so plug it into the other equation to solve for x)

-x + 3 = x + 5

(Add -x on both sides)

3 = 2x + 5

(subtract 5 from both sides)

-2 = 2x

(Divide by 2 on each side)

x = -1

I hope this helped!

8 0

3 years ago

Which expression has the same value as 4÷25?

Hatshy [7]

Answer:

We need the choices, since there are plenty equations with the same value.

Step-by-step explanation:

4/25=0.16

Whichever equation equals 0.16 is your answer.

6 0

4 years ago

Four times a number added to 3 times a larger number is 31. Seven subtracted from the larger number is equal to twice the smalle

aev [14]

Let the smaller number be x.
Let the bigger number be y.

$\begin{cases} &4x + 3y = 31 \tex{ ----- (1) } \\ &y- 7 = 2x \tex{ ----- (2) } \end{cases}$

Rearrange equation (2):
$\begin{cases} &4x + 3y = 31 \tex{ ----- (1) } \\ &y = 2x + 7 \tex{ ----- (2) } \end{cases}
$

Sub (2) into (1):

$4x + 3(2x + 7 ) = 31$
$4x + 6x + 21 = 31$
$10x + 21 = 31$
$10x = 10$
$x = 1$

Sub x = 1 into (2):

$y = 2x + 7$
$y = 2(1) + 7$
$y= 9$

Answer: The two numbers are 1 and 9.

5 0

3 years ago

Read 2 more answers

Will give brainliest plz help

Dominik [7]

Answer:

$\frac{(x+4)^2}{25}+\frac{(y+3)^2}{9}=1$