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4 years ago

Solve the system using elimination 7x+2y=10 -7x+y=-16

Mathematics

2 answers:

Naddika [18.5K]4 years ago

5 0

Answer:

x=2, y=-2

Step-by-step explanation:

7x+2y=10

-7x+y=-16

-------------------

0x + 3y = -6

Divide each side

3y/3 = -6/3

y = -2

Now find x

7x +2y = 10

7x + 2( -2) = 10

7x -4 = 10

Add 4 to each side

7x -4+4 = 10+4

7x= 14

Divide by 7

7x/7 = 14/7

x = 2

kenny6666 [7]4 years ago

5 0

Since one equation has a 7x and and the other equation has a -7x,

when we add the equations together, the x's will cancel out.

So we have 3y = -6 and y = -2.

To find x, plug -2 back in for y in either of the two original equations.

I've chosen to plug -2 into the first equation to get 7x + 2(-2) = 10.

Solving from here, x = 2.

So our final answer is the ordered pair (2, -2).

Now, check your answer.

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8_murik_8 [283]

Answer:

A. 8

Step-by-step explanation:

1kg=2.2

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3 years ago

Read 2 more answers

PLEASE HELP ME WITH THIS!!!

FrozenT [24]

Answer:

Step-by-step explanation:

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The scale factor is 1/2 and the length of AB is 4

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Hope this helps, Let me know if you have any questions !

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2 years ago

You buy a patty for $200 and pay 16% in tax (G.C.T). How much is money was paid to the cashier?

AleksAgata [21]

Answer:

$232

Step-by-step explanation:

Add 16% to 100% then multiply by 200

6 0

3 years ago

A ship sails 250km due North qnd then 150km on a bearing of 075°.1)How far North is the ship now? 2)How far East is the ship now

olga_2 [115]

Answer:

1) 288.8 km due North

2) 144.9 km due East

3) 323.1 km

4) 207°

Step-by-step explanation:

Bearing: The angle (in degrees) measured clockwise from north.

Trigonometric ratios

$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$

where:

$\theta$ is the angle
O is the side opposite the angle
A is the side adjacent the angle
H is the hypotenuse (the side opposite the right angle)

Cosine rule

$c^2=a^2+b^2-2ab \cos C$

where a, b and c are the sides and C is the angle opposite side c

-----------------------------------------------------------------------------------------------

Draw a diagram using the given information (see attached).

Create a right triangle (blue on attached diagram).

This right triangle can be used to calculate the additional vertical and horizontal distance the ship sailed after sailing north for 250 km.

Question 1

To find how far North the ship is now, find the measure of the short leg of the right triangle (labelled y on the attached diagram):

$\implies \sf \cos(75^{\circ})=\dfrac{y}{150}$

$\implies \sf y=150\cos(75^{\circ})$

$\implies \sf y=38.92285677$

Then add it to the first portion of the journey:

⇒ 250 + 38.92285677... = 288.8 km

Therefore, the ship is now 288.8 km due North.

Question 2

To find how far East the ship is now, find the measure of the long leg of the right triangle (labelled x on the attached diagram):

$\implies \sf \sin(75^{\circ})=\dfrac{x}{150}$

$\implies \sf x=150\sin(75^{\circ})$

$\implies \sf x=144.8888739$

Therefore, the ship is now 144.9 km due East.

Question 3

To find how far the ship is from its starting point (labelled in red as d on the attached diagram), use the cosine rule:

$\sf \implies d^2=250^2+150^2-2(250)(150) \cos (180-75)$

$\implies \sf d=\sqrt{250^2+150^2-2(250)(150) \cos (180-75)}$

$\implies \sf d=323.1275729$

Therefore, the ship is 323.1 km from its starting point.

Question 4

To find the bearing that the ship is now from its original position, find the angle labelled green on the attached diagram.

Use the answers from part 1 and 2 to find the angle that needs to be added to 180°:

$\implies \sf Bearing=180^{\circ}+\tan^{-1}\left(\dfrac{Total\:Eastern\:distance}{Total\:Northern\:distance}\right)$

$\implies \sf Bearing=180^{\circ}+\tan^{-1}\left(\dfrac{150\sin(75^{\circ})}{250+150\cos(75^{\circ})}\right)$

$\implies \sf Bearing=180^{\circ}+26.64077...^{\circ}$

$\implies \sf Bearing=207^{\circ}$

Therefore, as bearings are usually given as a three-figure bearings, the bearing of the ship from its original position is 207°

8 0

2 years ago

Read 2 more answers

Solve each system by elimination.

meriva

Answer:

4.)

a. x= -6 y-3

b. x= 5 y + 13

4 4

3.)

a. x= -4y + -8

5 5

b. x= 3 y+3

Step-by-step explanation:

4.)

a. 5x+6y=-15

Add -6y to both sides.

5x+6y+−6y=−15+−6y

5x=−6y−15

Divide both sides by 5.

5x ÷ 5= -6y-15 ÷5

x= -6 y-3

b. 4x - 5y=13

Add 5y to both sides

4x−5y+5y=13+5y

4x=5y+13

Divide both sides by 4

4x÷4= 5y+13÷4

x= 5 y + 13

4 4

5.)

a. (5x+4y=-8)

Add -4y to both sides

5x+4y+−4y=−8+−4y

5x=−4y−8

Divide both sides by 5

5x÷5= -4y-8÷5

x= -4y + -8

5 5

b. 2x - 3y = 6

Add 3y to both sides.

2x−3y+3y=6+3y

2x=3y+6

Divide both sides by 2.

2x÷2= 3y+6÷2

x= 3y+3

8 0

3 years ago