Solve the System of Equations
3x^2-5y^2= 22
2x^2+4y^2 = 22

Solve The System Of Equations3x^2-5y^2= 222x^2+4y^2 = 22

Answers

Answer 1

Lets try one way to solve this system. First, we want to isolate one of the unkown, lets choose y, so we need to remove x from an equation. In order to remove x from an equation, thats what we are going to do :

Line 1:

(3x² - 5y²) * 2 = 22 * 2

6x² - 10y² = 44

We simply multiplied Line 1 by the number 2, this doesn't change anything on the nature of Line 1.

Line 2:

(2x² + 4y²)*3 = 22*3

6x² + 12y² = 66

We simply multiplied Line 2 by the number 3, this doesn't change anything on the nature of Line 2.

Solving your system of equations is exactly the same thing as solving this new system of equation :

6x² - 10y² = 44

6x² + 12y² = 66

It is exactly the same. But it is easier now, because we can remove x from the equation simply by subtracting line 2 from line 1 :

L1 - L2 :

(6x² - 10y²) - (6x² + 12y²) = 44 - 66

6x² - 10y² - 6x² - 12y² = - 22

- 22y² = - 22

y² = 1

y = + 1 or y = - 1

We know have the value of y, we just have to replace it in the equation to solve the entire system :)

3x² - 5y² = 22

since y² will always be equal to one, wether y = 1 or y = - 1, we can write :

3x² - 5 = 22

3x² = 22 + 5

3x² = 27

x² = 27/3

x² = 9

x = + 3 or x = - 3

So the solutions are the following couples in the form (x,y) :

S = { (3 ; 1) , (-3;1) , (3 ; - 1) , (-3 ; -1))

Good Luck


Related Questions

why (0.0) (3.4) (6.8) (6,12) not a function

Answers

Answer:

Step-by-step explanation:

Look at the first elements of the four points:  {0, 3, 6, 6}.  The element 6 appears twice and is associated with two different second elements:  {8, 12}.  That tells us immediately that this is not a function.

what is 3 x 7 = x 3 ?

Answers

Answer:

7

Step-by-step explanation:

21=3x

x=7

Answer:

x = 7

Step-by-step explanation:

3 x 7 = x 3

21 = 3x

x = 21/3 = 7

plssss help picture down below

Answers

Answer:

it is (-4,1)

Step-by-step explanation:

Hope this helps:)

what is the product of... see attachment below

Answers

The answer is -7 (option A)

Steps are in the attachment.

_________

Hope it helps ✌

On a coordinate plane,△FGH is formed with the vertices at point F(0,−2), point G(1,0) , and point H(2,−3) . Which expression can be used to determine the perimeter, in units, of△FGH ?

A
(0−1)2+(−2−0)2−−−−−−−−−−−−−−−−√+(1−2)2+(0−(−3))2−−−−−−−−−−−−−−−−−−√+(2−0)2+(−3−(−2))2−−−−−−−−−−−−−−−−−−−√

B
(0−(−2))2+(1−0)2−−−−−−−−−−−−−−−−−−√+(1−0)2+(2−(−3))2−−−−−−−−−−−−−−−−−−√+(2−(−3))2+(0−(−2))2−−−−−−−−−−−−−−−−−−−−−√

C
(0+1)2−(−2+0)2−−−−−−−−−−−−−−−−√−(1+2)2−(0+(−3))2−−−−−−−−−−−−−−−−−−√−(2+0)2−(−3+(−2))2−−−−−−−−−−−−−−−−−−−√

D
(0+(−2))2−(1+0)2−−−−−−−−−−−−−−−−−−√+(1+0)2−(2+(−3))2−−−−−−−−−−−−−−−−−−√+(2+(−3))2−(0+(−2))2−−−−−−−−−−−−−−−−−−−−−√

Answers

Answer:

the answer i think is B

Step-by-step explanation:

Answer: B

Step-by-step explanation:

THEN c. If a || band line c is parallel to line a, then line b and c are?​

Answers

Answer: parallel

Step-by-step explanation:

For two lines to be parallel they must have the same slope.

Because a is parallel to b they must have the same slope.  Let's call that slope x.

Because c is parallel to b they must have the same slope.  Because the slope of b is x, the slope of c must be x.

Because the slope of both a and c are x, they must be parallel.

What is the slope of the line ( part 2 )

Answers

Answer:

[tex]m=-\frac{1}{2}[/tex]

Step-by-step explanation:

Same as last time, take any 2 points you want:

(0, 3) and (4, 1)

Use the slope formula to calculate the slope:

[tex]m=\frac{1-3}{4-0}\\m=\frac{-2}{4}\\m=-\frac{1}{2}[/tex]

On small problems like these, you don't really even need to calculate it like that. You can just look at the graph, see that it goes down 1 and over 2 from one point to the next, and have your slope that way. Again, rise over run. It "rises" by -1, and runs by 2. -1 over 2, there's your slope.

Î"RST was _____________, then dilated, to create Î"ZXY. Rotated reflected translated dilated.

Answers

Answer:

5

Step-by-step explanation:

Graph a right triangle with the two points forming the hypothenuse, Using the sides, find the distance between the two points, to the nearest tenth if necessary (3. -7) and 8. -3)

Answers

Answer:

That distance is 6.4

Step-by-step explanation:

The legs of the triangle form a right angle.  The bottom leg has length 8 - 3, or 5, and the vertical leg -3 - (-7), or 4.  Applying the Pythagorean Theorem:

(vertical leg)^2 + (horizontal leg)^2 = (hypotenuse)^2, which here is

4^2 + 5^2 = (hypotenuse)^2

This works out to 16 + 25, or 41.

The distance between these two points is d = √41, or d = 6.4

Yall i need help asap! please help​

Answers

3) 1010000

4) 1582

I helped

1. £1000 is invested for 2 years at 5% per annum with compound interest. Work out the total amount in the account after 2 years.

Answers

1000x1.05^2 =£1102.5

Answer:

A = £1102.50

Step-by-step explanation:

Use the compound amount formula:

A = P(1 + r)^t, where P is the principal, r is the interest rate as a decimal fraction, and t is the number of years.

Here A = £1000·(1 + 0.05)^2, which evaluates to  A = £1102.50

help with my math plz

Answers

Answer:

Step-by-step explanation:

The side is S= 5 cm , and the area is A= S² = 5²= 25

If the side would be doubled will be S= 5*2 = 10 cm, and the area A= 10²=100

Compare the area of S=5 to area of S=10 , 100 = 4*25

Conclusion:

If we double the side the area is 4 times greater.

does anyone know what the answers are to this question? thank you sm if you help!! :)

Answers

u’ should equal to 23
v’ should be equal to 4

I’m not exactly sure but please do feel free to correct any mistakes I made.

List three negative numbers that are greater than - 9​

Answers

Answer:

the answer to your question is -6 -5 -3 but there are more.

Answer:

there are infinite but you can take any numbers from the right one that are

-8,-7,-6,-5,-4,-3,-2,-1,0,1,2....

Find the unit rate.

12 laps in 30minutes

Answers

Answer:

0.4/1

Step-by-step explanation:

We want a unit rate where

1 is in the denominator,

so we divide top and bottom by 30

1 dm = _______ cm what answer of this

Answers

Answer:

1dm = 10cm

Simple as it is

Answer:

The term “Deci” means one-tenth, and therefore decimetre means one-tenth of a meter. Since a meter is made up of 100 cm, one-tenth of 100 cm is 10 cm. Thus one decimeter measures 10 cm.

Step-by-step explanation:

hope it's help!

#letusstudy

#Staysafe!

#brainly

Annelise buys a car that is one year old for $13600.
The value of this car has reduced by 15% of the value when it was new.
Calculate the value of the car when it was new.

Answers

Answer:

$16000

Step-by-step explanation:

Initial value is x, current value is $13600, price reduction by 15%.

x - 15% = 13600x - 0.15x = 136000.85x = 13600x = 13600/0.85x = 16000


Type the expression that results from the following series of steps:
Start with z and add 5.

Answers

the answer will be z+5

Please give me the answer

Answers

Answer:

8%

If you need the work comment on this post.

Solve and graph each of the following. Show your work to receive full credit.5x – 6 – 8x ≤ 9

Answers

Answer: x> or equal to -5

Step-by-step explanation:

5x – 6 – 8x ≤ 9

Combine the lioe numbers

-3x-6≤ 9

+6 to both sides

-3x≤ 15

Divide by a -3 to both sides

X>or equal to -5

Hope that helps

7x-15y=2 , x+2y=3 By subtition method​

Answers

Answer:

([tex]\frac{49}{29},\frac{19}{29}[/tex])

Explanation:

7x - 15y = 2  (1)

x + 2y = 3 (2)

x + 2y = 3

x + 2y - 2y = 3 - 2y

x = 3 - 2y  (3)

Substitute (3) to (1)

7x - 15y = 2

7(3 - 2y) - 15y = 2

21 - 14y -15y = 2

21 - 21 - 29y = 2 - 21

-29y = -19

y = [tex]\frac{19}{29}[/tex]  (4)

Plug (4) into (2)

x + 2y = 3

x + 2[tex]\frac{19}{29}[/tex] = 3

x + [tex]\frac{38}{29}[/tex] = 3

x = 3 - [tex]\frac{38}{29}[/tex]

[tex]x = \frac{87}{29}-\frac{38}{29} =\frac{49}{29}[/tex]

([tex]\frac{49}{29},\frac{19}{29}[/tex])

(−4/3)⋅(−1/3)⋅1.2 answer plz

Answers

Answer:

= .533

Step-by-step explanation:

(−4/3)•(−1/3)= .44

.44•1.2=.533

A backback originally costs $35 it is on sale for $22.75 find the percent of decrese

Answers

Answer $12.25

Step-by-step explanation: edmentum

x3+y3+z3=k What does this equation mean please?

Answers

Answer:

Sum of cubes problem

Step-by-step explanation:

The equation x3+y3+z3=k is sum of cubes problem. While seemingly straightforward, the equation becomes exponentially difficult to solve when framed as a "Diophantine equation" a problem that stipulates that, for any value of k, the values for x, y, and z must each be whole numbers.

Answer:

it means x to the third power, plus y to the third power, plus z to the third power, equals some number (k).

Step-by-step explanation:

-4x + 60 < 72 or 14x + < -31

Answers

x=31/14

Step-by-step explanation:

I did the second one btw

Suzanne has 15 books and will buy 3 more each month. Jack has 57 books and will sell 4 books each month. After how many months will they have the same number of books? How many will that be?

Answers

They would both have the same number of books after 6 months.

The number of books they would have is 33.

This expression can be used to determine the number of books Suzanne would have after x months: 15 + 3x

This expression can be used to determine the number of books Jack would have after x months: 57 - 4x

In order to determine the month in which both people would have the same number of books, equate both expressions.

15 + 3x = 57 - 4x

Combine similar terms

3x + 4x = 57 - 15

7x = 42

Divide both sides b y 7

x = 6

Number of books they would have : 15 + 3(6) = 15 + 18 = 33

A similar question was answered here: https://brainly.com/question/21014980?referrer=searchResults

ben bolwed 138 and 208 in his first two games. What must he bowl in his third game to have an average of at least 170?

Answers

Answer:

at least 164

Step-by-step explanation:

Let the third score = x.

(138 + 208 + x)/3 ≥ 170

x + 346 ≥ 510

x ≥ 164

Answer: at least 164

10, 18, 26, 34, 42, ...

What is the 15th term of this Arithmetic Sequence

Answers

Answer:

a₁₅ = 122

Step-by-step explanation:

Arithmetic sequence formula:

[tex]a_n=a_1+(n-1)d[/tex]

where aₙ is the nth term, a₁ is the first term, n is the index, and d is the rate of change.

For your given sequence:

[tex]10, 18, 26,34,42,...[/tex]

a₁ is 10

n is 15 (15th term)

d is 8 (each term increases by 8 over the last)

Plug those 3 variables in, and solve for a₁₅:

[tex]a_n=a_1+(n-1)d\\a_1_5=10+(15-1)8\\a_1_5=10+(14)8\\a_1_5=10+112\\a_1_5=122[/tex]

Use substitution to solve the system of equations algebraically.
x² + y² = 32
y = x
One solution to the system of equations is (4,4).
The other solution to the system of equations is

Answers

Answer:

(-4,-4)

Step-by-step explanation:

Since y=x,plug in x for y in equation 2

x²+x²=32

2x²=32

x²=16

x=√16=±4

So one solution is (4,4) and another is (-4,-4)

Answer:

i really cant tell you

Step-by-step explanation:

sorry

Use the distributive property to
expand the expression below.
6(2a – 3) = [?]a - [ ]

Answers

Answer:

12a - 18

Step-by-step explanation:

6 x 2 = 12 (then add the "a" = 12a

6 x 3 = 18

put the minus in the middle then get

12a- 18

Other Questions
Identify one component of a social media information system (SMIS) that is not included in other information systems. which of the following is true about mental health and divorce ?A.women experience more difficulties than menb. men experience more difficulties than womenc. middle children experience more difficulties than first born children d. every member of a family experience the difficulties in a different way 3. Mention any two factors that affect the climate of an area. Albert einstein (1)______ born in germany in 1879. In 1895, he (2)______to school in switzerland. After college, he (3)______ in switzerland for 28 years, and then he (4)______ to the us in 1933. He (5)______ in 1955 in the us. the marine corps is necessary and why Potassium metal reacts with water according to the following balanced equation.2 K(s) + 2 H2O(l) 2 KOH(aq) + H, (8)If one mole of potassium reacts in this manner, how many moles of water are consumed? Sophie-Louise says that tomorrow she will visit the cathedral in Bel' Mangrov square.A. vraiB. faux I WILL MARK YOU BRAINLY IF YOU ANSWER CORRECTDuring which period did Confucius live?A) the reign of the three sages of oldB) the Warring States periodC) the decline of the Shang dynastyD) the Qin dynasty Someone please help will mark as brainliest Need help quickly (Finding angle measures using triangles) Bianca deposits $3,000 in a savings account earning 4.25% simple interest per year. Part A How much interest will Bianca earn for a period of 3 years? please help methis question is too much hard I think that my brain stopped working The selling price of an item is 720 it is marked down 30% but the sale price is still marked up from the cost of 420 find the mark up from the cost of the sale price The Park Plaza Hotel is located in________ A. Princeton B. New York C. Grover's Mill D. Trenton Explain the concept of interest Stems are important plant structures because they _________.A. are the main sites of photosynthesis for plantsB. are the only site of water and nutrient transportC. allow plants to absorb water and nutrients from the soilD. give the plant structure and support It is also known as jingju lianpu that is done with different colors in accordance with the performing characters, personality and historical assessment. What is the difference between structural and compositional layers of the Earth'sinterior? respect (e.g. an individuals personal religious beliefs about the type of food they can eat in hospital) 14. They are symbols that denote silence and give the performer time to relax. * O a. notes O b.rests O c. time signatures