All categories

2 years ago

Please solve the system of equations !!

Mathematics

1 answer:

Dominik [7]2 years ago

6 0

$\bold{\huge{\red{\underline{ Solution}}}}$

$\bold{\underline{ We \: have\: given :-}}$

$\sf{ 2x + 7y = 3 ...eq(1 ) }$

$\sf{ x = -4y ...eq(2) }$

Here, we will use the substitution method for solving the above equations.

$\bold{\underline{Subsitute \: eq(1)\:in \: eq(2)}}$

$\sf{ 2(-4y) + 7y = 3 }$

$\sf{ -8y + 7y = 3 }$

$\sf{ - y = 3 }$

$\sf{ y = - 3. ...eq( 3) }$

$\bold{\underline{Subsitute \: eq(3)\:in \: eq(2)}}$

$\sf{ x = -4(-3) }$

$\sf{ x = 12 }$

$\sf{\blue{ Hence, \: The \:value \:of \:x \:and \:y \:is\: 12\: and \:-3}}$

You might be interested in

3(2-4x)=-30 with justfity steps

alexandr1967 [171]

Answer:

x = 3

Step-by-step explanation:

3(2 - 4x) = -30

=>6 - 12x = -30

=> 12x = 36

=> x = 3

7 0

3 years ago

GUYS I NEED HELP ASAP

vovangra [49]

Answer:

$A=2400ft$

Step-by-step explanation:

A rectangle is a closed planer quadrilateral with four right angles and its opposite sides are the same length. The fence around it including the gates is 200 feet long, so basically they are providing the perimeter of the rectangle. The perimeter of a rectangle is equal to the sum of all its sides. Hence:

$Perimeter=w+h+w+h=2w+2h\\\\Where:\\\\w=Width\\h=Height$

The ectangular playground is 40 feet wide, so:

$w=40ft$

Therefore:

$Perimeter=2w+2h\\\\200=2(40)+2h\\\\200=80+2h$

Solving for h:

$2h=200-80\\\\2h=120\\\\h=\frac{120}{2} \\\\h=60ft$

The area of a rectangle is equal to the product of two of its contiguous sides, hence:

$A=wh\\\\A=(40)(60)=2400ft$

I attached you a picture of the rectangle

5 0

3 years ago

In a city the distance between the library and the police station is 3 miles less than twice the distance between the police sta

aliya0001 [1]

Answer:

The distance between the police station and the fire station is 4 miles

Step-by-step explanation:

* Lets study the situation in the problem to solve it

- In the city there are three places, library , police station and fire station

- The distance between the library and the police station is 3 miles

less than twice the distance between the police station and the

fire station

- The distance between the library and the police station is 5 miles

* Lets change all of these situation to equations

# Let the distance between the library and the police station is x

# Let the distance between the police station and the fire station is y

∵ The distance between the library and the police station (x) is 3 miles

less than twice the distance between the police station and the

fire station (y)

∴ x = 2y - 3

∵ The distance between the library and the police station is (x) 5 miles

∴ x = 5

- Substitute the value of x in the equation above

∵ x = 2y - 3

∵ x = 5

∴ 5 = 2y - 3 ⇒ add 3 to both sides

∴ 8 = 2y ⇒ divide both sides by 2

∴ 4 = y

∵ y is the distance between the police station and the fire station

∴ The police station is 4 miles apart from the fire station

* The distance between the police station and the fire station is 4 miles

7 0

3 years ago

You are making meat loaf with yield: 50, 4oz portions what is the total recipe cost

slamgirl [31]

Answer:

$200oz$

Step-by-step explanation:

The question says that there are $50$ portions that are $4oz$ each.

Write an equation

$(50)4oz$

Simplify

$200oz$

3 0

3 years ago

Through: (1,-5), perpendicular to y=18x+26

stiks02 [169]

Answer:

Step-by-step explanation:

If you're asking for the equation of a line that goes through (1,-5) and is perpendicular to y=18x+26 here's what you do.

1. find the slope of the new line by taking the negative reciprocal of the slope of the first line ( $-\frac{1}{18}$ )

2. plug in the point (1,-5) and the new slope into the point slope form equation

$y_{2} -y_{1}=m(x_{2}-x_{1})$

3.Now that you have y-(-5)= -1/18(x-1) simplify

3.a y-(-5)= -1/18x + 1/18

3.b y=-1/18x - 89/18

4. final equation you get is y = -1/18 - 89/18

8 0

4 years ago