solve the simultaneous equation

x+2y=5
x²-y²=-3​

Answers

Answer 1

Answer:

y = 14/3 and 2

x = -13/3 and 1

(-13/3, 14/3) and (1, 2)

Step-by-step explanation:

[tex]x + 2y = 5 - - - (a) \\ {x}^{2} - {y}^{2} = - 3 - - - (b)[/tex]

for equation (a)

make x the subject of the formular:

[tex]x = 5 - 2y - - - (c)[/tex]

for equation (b)

[tex] {x}^{2} - {y}^{2} = - 3[/tex]

substitute for x as 5 - 2y in equation (b):

[tex] {(5 - 2y)}^{2} - {y}^{2} = - 3 \\ (25 - 20y + 4 {y}^{2} ) - {y}^{2} = - 3 \\ 25 - 20y + 3 {y}^{2} = - 3 \\ {3y}^{2} - 20y + 28 = 0 \\ (3y - 14)(y - 2) = 0[/tex]

therefore,

[tex]y = \frac{14}{3} \: \: and \: \: 2[/tex]

substitute for all values of y in equation (c):

for y = 14/3:

[tex]x = 5 - 2( \frac{14}{3} ) \\ \\ x = 5 - \frac{28}{3} \\ \\ x = - \frac{13}{3} [/tex]

for y = 2:

[tex]x = 5 - 2(2) \\ x = 5 - 4 \\ x = 1[/tex]

Answer 2

Answer:

(1, 2)

(-13/3, 14/3).

Step-by-step explanation:

x + 2y = 5

x² - y² = -3​

From the first equation x = 5 - 2y

Substitute for y in the second equation:

(5 - 2y)^2 - y^2 = -3

25 + 4y^2 - 20y - y^2 = -3

3y^2 - 20y + 28 = 0

Factoring:-

(3y - 14(y  -  2)   = 0

y = 2, 14/3.

So when y = 2, x = 5 - 2(2) = 1.

When y = 14/3, x = 5 - 2(14/3) = -13/3.

Checking the results in the second equation:

(1, 2):-

1^2 - 2^2 = -3    Correct.

(-13/3, 14/3):-

(-13/3)^2 - (14/3)^2 = -3   Correct.


Related Questions

Find the value of x and QR if Q is between P and R.

PQ=2x
QR=x + 2
PR= 5x -10

Answers

Answer:

2x+x+2=5x-10

3x+2=5x-10

-3x -3x

2=2x-10

+10 +10

12=2x

2x/2=x 12/2=6

x=6

QR=x+2

6+2=8

QR=8

The value of x is 6 and the value of QR will be 8 units.

What is a line segment?

A line segment in geometry is a section of a line that has two clearly defined endpoints and contains every point on the line that lies within its confines.

Given that the value of x and QR if Q is between P and R.

PQ=2x

QR=x + 2

PR= 5x -10

The value of x will be calculated as below:-

2x+x+2=5x-10

3x+2=5x-10

2=2x-10

12=2x

x = 12 / 2

x =6

The value of QR will be calculated as below:-

QR=x+2

6+2=8

Therefore, the value of x is 6 and the value of QR will be 8 units.

To know more about line segments follow

brainly.com/question/2437195

#SPJ2

Compare -3 and -5 using <,>, Or =

Answers

Answer:

-3 > -5

Step-by-step explanation:

If there’s a higher number that is negative, let’s say that 5 is greater than 3 but if 5 is negative it can’t be greater than 3 even if 3 is a negative as well.

Hope this helps

- Is this a function? Why or why not?
Independent
Variable
Dependent
Variable
3
6
4
15
+8
12
14
agen 20
22
11
asking for

Answers

9514 1404 393

Answer:

  a) yes (a function)

  b) no (not a function)

Step-by-step explanation:

A functional relationship will have only one value of dependent variable for each value of independent variable. That is, the column on the left can only have one arrow tail per item.

__

a) is a function. Each independent variable maps to one dependent value

b) not a function. Independent variable values 7 and 30 map to two values each.

The circle has center O. Its radius is 9 ft, and the central angle a measures 50°. What is the area of the shaded region?
Give the exact answer in terms of it, and be sure to include the correct unit in your answer.

Answers

Answer:

35.34305555555

Step-by-step explanation:

You must calculate the percentage taken out of the circle by the shaded region. This would be about 13.8%. Then you take the overall area of the circle and multiply it by the percentage. This should give you your answer.

REMEMBER TO ROUND IF YOU ARE SUPPOSED TO, THERE IS NO INDICATION ON BRAINLY. WITHOUT ROUNDING YOU CAN GET THE ANSWER WRONG.

what is the midpoint of (4,5) and (9,17)

Answers

Answer:

Step-by-step explanation:

Midpoint formula: ( (x1+x2)/2, (y1+y2)/2)

where (x1, y1) and (x2, y2) are our points

Let (x1, y1) = (4, 5)

and (x2, y2) = (9, 17)

x1 = 4

x2 = 9

y1 = 5

y2 = 17

Then ( (4+9)/2, (5+17)/2 ) = (13/2, 22/2) = (13/2, 11)

Convert 99000 milligrams into pounds. Round your answer to the nearest hundredth.

Answers

Answer:

0.22

Step-by-step explanation:

Find the 14th term of the geometric sequence 2,4,8

Answers

16348

The pattern is times 2

2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384

what does equal
(27/64)-2/3=

Answers

Look at the picture
Answer: -47/192
Steps: (27/64-2/3
81-128/192
Hope that helps

Choose the correct simplification of (9x3y2)2.

Answers

Answer:

The Correct simplification is: (3².2x³y²)

Answer:

81x^6y^4

Step-by-step explanation:

Its midpoint please help

Answers

Answer:

[tex]thank \: you[/tex]

Please help asap thank you! I'll mark brainlyest​

Answers

Answer:

3

Step-by-step explanation

add all of the numbers then divide by the amount the numbers you added

in this situation it is 1+2+3+4+5=15 divided by 5 equals 3. Hoped this helped. pls give brainliest

Find X and Y. Please Help I will reward you with 95 points

Answers

Answer:

45° and 20°

Step-by-step explanation:

2x is supplementary with the right angle and 3y is supplementary with 6y, as same side interior angles.

Therefore:

2x + 90 = 1802x = 90x = 45

And

3y + 6y = 1809y = 180y = 20

[tex]\\ \rm\longmapsto 2x+90=180[/tex]

[tex]\\ \rm\longmapsto 2x=180-90[/tex]

[tex]\\ \rm\longmapsto 2x=90[/tex]

[tex]\\ \rm\longmapsto x=90/2[/tex]

[tex]\\ \rm\longmapsto x=45°[/tex]

Now

[tex]\\ \rm\longmapsto 3y+6y=180[/tex]

[tex]\\ \rm\longmapsto 9y=180[/tex]

[tex]\\ \rm\longmapsto y=180/9[/tex]

[tex]\\ \rm\longmapsto y=20[/tex]

-11+x(-7) when x= 4
Please help ASAP

Answers

Step-by-step explanation:

-11+x(-7)

when x= 4, then

-11+x(-7)

-11+4(-7)

-11+(-28)

-11-28

-39

*7th grade math* ts confusing yall.

Answers

It should already be correct

The additive inverse of 5/8 is 5/-8 (m)

Additive inverses equal each other out when added
5/8 + m = 0

Please mark brainliest

More help Pls (am also giving away points).

Answers

Answer:

Bot #11

Step-by-step explanation:

If you picked bot 12 in 5 second it produces 21 clicks which means if you add another 5 second it will be 10 second with 42 clicks. But, if you pick the bot with 17 clicks per 4 second, 8 seconds it will already be 34 clicks and 10 seconds half of 17 is  8/5 which in 10 seconds it produces 42.5 which shows the first bot produces more.

Solve this please, I can't understand the question, so the answer with the working would be appreciated.

Answers

The pyrite cube is, well, a cube, so it has a side length s such that the area of its base is

s ² = 5.76 cm²

which means

s = √(5.76 cm²) = 2.4 cm

Then its volume is

s ³ = 13.824 cm³

Pyrite is also known as "fool's gold" because it looks a lot like gold. So if gold has a unit price of €785/cm³, then a pyrite cube with volume 13.824 cm³ could be mistaken for a gold cube of the same volume, which would sell for a price of

(€785/cm³) × 13.824 cm³ = €10,851.80

simplify 6^2n+1x9^nx4^2n÷18^nx2^nx12^2n please help ..Thank you​

Answers

Answer:

[tex]2^{-4 n}\times3^{-2 n} + 3^{-2 n}\times4^{-n}[/tex]

Step-by-step explanation:

Assuming you meant [tex]\frac{6^{2n}+1*9^n*4^{2n}}{18^n*2^n*12^{2n}}[/tex], the answer is [tex]2^{-4 n}\times3^{-2 n} + 3^{-2 n}\times4^{-n}[/tex].

What is six hundred five thousand, five hundred written in standard form

Answers

605,500 in the standard form is 6.055 × 10^5

**3. What is the y-intercept of the line that has a slope of
-4 and passes through the point (4, -6)?

Answers

Answer:

10

Step-by-step explanation:

We'll first write in point-slope form:

y - y1 = m(x - x1)

where (x1, y1) is our point and m is our slope.

Then convert into slope-intercept form to make it easier to find the y-intercept.

y - (-6) = -4(x-4)

y + 6 = -4(x-4)

y + 6 = -4x + 16

y = -4x + 10

Now that we've put the equation in slope-intercept form, we see that our b-value

y = mx + b

b = 10, so our y-intercept is 10

Pls help I’m having trouble

Answers

Answer:

find the area of each side of the shapes and add make sure it's in square centimeters

Can you solve this? step by step ,if possible

Answers

Answer:

Ans:

Step-by-step explanation:

Let, the required number=n

Then, That number is actually n(n-1)

For e.g 8(8-1)=56 divided by 8=7

You Understood it.

I need help with this question.

Answers

Answer:

If I had guess, always equal since absolute numbers are always positive.

Help please !!!!!!!!!!

Answers

Answer:

Solving for x:

x= -y-5

Solving for y:

y= -x-5

Step-by-step explanation:

There is a vent diagram - it asked 30 students if they have a cat or dog. 21 have a dog. 16 have a cat. 8 have a dog, but not a cat. How would I put this on a two circle Venn diagram?

Answers

dog intersect cat = 13

only cat= 3

A certain forest covers an area of 4900 km². Suppose that each year this area decreases by 7%. What will the area be after 8 years?
Use the calculator provided and round your answer to the nearest square kilometer.

Answers

Answer:

area after 8 years is 2156km²

Step-by-step explanation:

Area of forest=4900 km²

decrease in area in 1 year=4900km² × 7%

decrease in area in 1 year= 343km²

decrease area in 8 years=343km² × 8

=2744km²

Remaining area= (4900-2744)km²

=2156km²

Note:If you have any question about it please ask.


ANYONE KNOW HOW TO DO THIS IM BEGGING

Answers

1 is reflection
Basically u got to look at what happens to the original shape

Find seven ordered pairs to the equation y=x^2-4

Answers

Answer:

(1,-3)

(2,0)

(3,5)

(4,12)

(0,-4)

(-1,-3)

(-2,0)

Which equation represents a population of 250 animals that decreases at an annual rate of 21% ?

A. p = 250(1.21)
B. p = 250(1.79)
C. p= 250(0.79)
D. p=250(0.21)

Answers

Answer: Choice C.  p = 250(0.79)^t

Work Shown:

p = a*b^t

p = a*(1+r)^t

p = 250*(1+(-0.21))^t

p = 250(0.79)^t

Note that r = -0.21 is negative to indicate we have exponential decay.

Given m||n, find the value of x.
+
mm
(6x-20)
(6x-4)
PLS HELP ASAP

Answers

Answer:

17°

Step-by-step explanation:

SEE THE IMAGE FOR SOLUTION

HOPE IT HELPS

HAVE A GREAT DAY

Answer:

x=17

Step-by-step explanation:

The angles add to 180

6x-20 + 6x-4 = 180

Combine like terms

12x -24 =180

Add 24 to each side

12x = 180+24

12x = 204

12x/12 = 204/12

x =17

john has a mass of 54 kg ,60grams. how many grams is that

Answers

Answer:

54,060g

Step-by-step explanation:

1kg=1000,

therefore 54kg= (54x1000)

                        = 54000+60

                        = 54060g

54000+60

=54060
The answer is
Other Questions
Select the letter of the correct answer.The article talks mainly aboutA. unusual marketing stunts that have been done inspaceB. different ways that companies market their productsC. different ways that companies get customers to helpthemD. unusual marketing stunts that have gone wrong George plans to cover his circular pool for the upcoming winter season. The pool has a diameter of 20 feet and the cover extends 12 inches beyond the edge of the pool. A rope runs along the edge of the cover to secure it in place.a. What is the area of the pool cover?b. What is the length of the rope?You must show all of your work to receive credit URGENT!!1-84. Find the perimeter and area of each figure.9.85 m15 m9 m Define normal distribution. In the 20072008 season,Dwayne Wade made 439 field goals outof 937 attempts. What was DwayneWades ratio of successful field goals toattempts? Write your answer as both afraction in simplest form and a decimalrounded to the nearest thousandth. A 180-inch pipe is cut into two pieces.one piece is three times the length of the other.find the length of the shorter piece. When 1 carbon atom combines with2 oxygen atoms, the resulting substance is called a(n) Help anyone can help me do this question 2,I will mark brainlest. 8^2 x 6{4 + 8^2(10 - 6)}^2 Which of the following sentences contains a comma error? Group of answer choices With the moving van packed, my friend had to say goodbye. Everyone, even our neighbors, came to our Super Bowl party. The packages became too heavy for me, I dropped them. My sweet, quiet father surprised us with his outburst yesterday. Can someone do number 4 please. and show the work if you can 3. Why should a goal be measurable? A. to create a sense of urgencyB. to create motivationC. to provide exact reasonsD. to provide benchmarks the locations of a house, market, and library from a right triangle as shown in the diagramPlease help quick!! What correctly describes the melting of a solidThe particles in the solid LOSE enough energy to OVERCOME the interactions between the particles The particles in the solid GAIN enough energy to FORM the interactions between the particlesThe particles in the solid GAIN enough energy to OVERCOME the interactions between the particlesThe particles in the solid LOSE enough energy to raise the temperature of the solid enough to turn it into aliquid Economically, a "want" is something __________. Will give brainliest answer please help An interior angle of a regular polygon measures 170. How many sides does it have? Determine the geometric mean of 8 and 12, to the nearest tenth.A) 10.0B) 4.5C) 48.0D) 9.8 Fuentes no renovables de la naturaleza Write this in set notation [-13; 4 )