All categories

3 years ago

Solve the simultaneous equations 4x+8y=-4 2y-5x=23

Mathematics

2 answers:

ad-work [718]3 years ago

8 0

Answer:

x = -4, y = 3/2

Step-by-step explanation:

simplify the 1st equation by dividing each term by 4 to get:

x + 2y = -1

-5x + 2y = 23

Subtract to get: 6x = -24

x = -4

find 'y': 2y - 5(-4) = 23

2y + 20 = 23

2y = 3

y = 3/2

Mama L [17]3 years ago

6 0

Answer:

y is equal to 1.5, and x is equal to -4

Step-by-step explanation:

given:

$4x + 8y = -4$

$2y - 5x = 23$

We can start by factoring 4 out of the first equation:

$x + 2y = -1$

Now let's multiply it by -5:

$-5x - 10y = 5$

We'll rearrange the other equation to match that (just for clarity):

$-5x + 2y = 23$

Now let's subtract the modified equation from that:

$\begin{array}{c}-5x + 2y = 23\\-5x - 10y = 5\\ \ \ \ \ \ \ \ \ \ \ 12y = 18\end{array}$

So y is equal to 18/12, or 1.5

Let's plug that into one of the first equations and see what we get:

$2y - 5x = 23\\2(1.5) - 5x = 23\\3 - 5x = 23\\-5x = 20\\x = -4$

Giving us an x value of negative four. Let's plug that into the other equation to confirm:

$4x + 8y = -4\\4(-4) + 8y = -4\\-16 + 8y = -4\\-4 + 2y = -1\\2y = 3\\y = 1.5$

That matches up, so our answer is correct.

You might be interested in

If i had a kid on october 6th and another 12 months later how old would the first kid be

zepelin [54]

Answer:

3 months old

Step-by-step explanation:

9 months for birth

and then the other 3 months is the age.

5 0

3 years ago

Read 2 more answers

A disc has a diameter of 23 cm. The inner hole in the disc has a radius of 2 cm. Find the circumference of both the inner hole a

mel-nik [20]

Answer:

Inner hole: 13 cm; Whole disc, 72 cm

Step-by-step explanation:

Connexus 2021

3 0

3 years ago

Find the circumference of each circle from the given radius or diameter

g100num [7]

Answer: 7) 50.27 8) 251.33 9) 235.62 *These answers were calculated using the true value of pi, not 3.14*

4 0

3 years ago

Read 2 more answers

Please help me answer this question

stealth61 [152]

The value of dy/dx for the functions are

(i) $\frac{dy}{dx} = 4x^{2}sin2x.cos2x+ 2x. sin^{2}2x$

(ii) $\frac{dy}{dx} =\frac{- y(1+3x^{2})}{2x(1+x^{2}) }$

<h3>Differentiation</h3>

From the question, we are to determine dy/dx for the given functions

(i) $x^{2} sin^{2}2x$

Let $u = x^{2}$

and

$v = sin^{2} 2x$

Also,

Let $w= sin2x$

∴ $v = w^{2}$

First, we will determine $\frac{dv}{dx}$

Using the Chain rule
$\frac{dv}{dx} = \frac{dv}{dw}.\frac{dw}{dx}$

$v = w^{2}$

∴ $\frac{dv}{dw} =2w$

Also,

$w= sin2x$

∴ $\frac{dw}{dx} =2cos2x$

Thus,

$\frac{dv}{dx} = 2w \times 2cos2x$

$\frac{dv}{dx} = 2sin2x \times 2cos2x$

$\frac{dv}{dx} = 4sin2x . cos2x$

Now, using the product rule

$\frac{dy}{dx} = u\frac{dv}{dx} + v\frac{du}{dx}$

From above

$u = x^{2}$

∴ $\frac{du}{dx}=2x$

Now,

$\frac{dy}{dx} = x^{2} (4sin2x.cos2x)+ sin^{2}2x (2x)$

$\frac{dy}{dx} = 4x^{2}sin2x.cos2x+ 2x. sin^{2}2x$

(ii) $xy^{2}+y^{2}x^{3} +2=0$

Then,

$x.2y\frac{dy}{dx}+ y^{2}(1)+y^{2}.3x^{2} + x^{3}.2y\frac{dy}{dx} +0=0$

$2xy\frac{dy}{dx}+ y^{2}+3x^{2}y^{2} + 2x^{3}y\frac{dy}{dx} =0$

$2xy\frac{dy}{dx}+2x^{3}y\frac{dy}{dx} =- y^{2}-3x^{2}y^{2}$

$\frac{dy}{dx} (2xy+2x^{3}y)=- y^{2}(1+3x^{2})$

$\frac{dy}{dx} =\frac{- y^{2}(1+3x^{2})}{2xy+2x^{3}y}$

$\frac{dy}{dx} =\frac{- y^{2}(1+3x^{2})}{2xy(1+x^{2}) }$

$\frac{dy}{dx} =\frac{- y(1+3x^{2})}{2x(1+x^{2}) }$

Hence, the value of dy/dx for the functions are

(i) $\frac{dy}{dx} = 4x^{2}sin2x.cos2x+ 2x. sin^{2}2x$

(ii) $\frac{dy}{dx} =\frac{- y(1+3x^{2})}{2x(1+x^{2}) }$

Learn more on Differentiation here: brainly.com/question/24024883

#SPJ1

8 0

2 years ago

How many feet will a person run during a 5 kilometer race?

salantis [7]

16,404 feet is the answer

6 0

3 years ago

Read 2 more answers