All categories

3 years ago

What is the solution to the system of equations?

Mathematics

1 answer:

Savatey [412]3 years ago

7 0

Answer:

The solution of the system of equations is (4 , 2) ⇒ 1st answer

Step-by-step explanation:

* Lets explain how to solve the system of equations

- In the system of equations there are two equations in two variable

x and y

- There are two ways to solve them:

# Substitution method: substitute one variable from one equation

into the other equation, so the equation will have one variable so

we can solve it

# Elimination method: we try to eliminate on variable from both

equation by addition or subtraction to get one equation in one

variable so we can solve it

* Lets solve the problem

∵ The system of equations has:

x + y = 6 ⇒ (1)

x = y + 2 ⇒ (2)

- We will use the substitution method because the second equation

is x in terms of y

- Substitute equation (2) in equation (1)

- That mean replace x by y + 2

∵ (y + 2) + y = 6

- Add the like terms in the left hand side

∴ (y + y) + 2 = 6

∴ 2y + 2 = 6

- Subtract 2 from both sides

∴ 2y = 4

- Divide both sides by 4

∴ y = 2

- Now substitute the value of y in equation (2)

∵ x = y + 2 ⇒ (2)

∴ x = 2 + 2 = 4

∴ x = 4

∴ The solution of the system of equations is (4 , 2)

You might be interested in

Parabolas. Please help me

olganol [36]

x² = 16 y
x = 0
(x + 4)² = 2/3 (y - 2)
Gayle identifies that the vertex of the parabola is (3, -1) . The parabola opens right, and the focus is 3 units away from the vertex. The directrix is 6 units from the focus. The focus is the point (6, -1). The directrix of the equation is x = 0.
(y - 6)² = 4p (x - 3)

Step-by-step explanation:

1. First figure

We plot the parabola as given in the attached diagram.

As it is facing upwards, the equation goes as x² = 4py

where, p = 4 (refer the attached diagram)

x² = 4py

x² = 4 (4) y

∴, standard form of parabola is x² = 16 y

2. Second figure

(y + 3)² = 4 (x - 1)

Comparing the given equation with the standard form

(y - k)² = 4p (x - h)

Now from this equation we get to know that

h = 1

p = 1

Directrix is x = (h - p)

So, x = 0

3. Third figure

3x² + 24x - 2y + 52 = 0

3x² + 24x = 2y - 52

3 (x² + 8x) = 2 (y - 26)

(x² + 8x) = 2 (y - 26) / 3

Adding 16 on both sides,

x² + 8x + 16 = 2 (y - 26) / 3 + 16

(x + 4)² = 2/3 y - 52/3 + 16

(x + 4)² = 2/3 y - 4/3

(x + 4)² = 2/3 (y - 2)

4. Fourth figure

(y + 1)² = 12 (x - 3)

Comparing the given equation with the standard form

(y - k)² = 4p (x - h)

Now from this equation we get to know that

k = -1

h = 3

p = 3

Gayle identifies that the vertex of the parabola is (3, -1) . The parabola opens right, and the focus is 3 units away from the vertex. The directrix is 6 units from the focus. The focus is the point (6, -1). The directrix of the equation is x = 0.

5. Fifth figure

Focus = (2, 6)

Directrix is x = 4

Therefore, it follows the standard form

(y - k)² = 4p (x - h)

Directrix is given by x = h-p = 4

Focus is given by (h + p, k) = (2, 6)

Solving for (h - p) = 4, (h + p) = 2

2 - p - p = 4

-2p = 2

p = -1

Hence, h = 3

Therefore, the standard form can be written as

(y - 6)² = 4p (x - 3)

7 0

3 years ago

Hi can you please help me

Licemer1 [7]

For this you need to know your angles in parallel lines.
3y will equal 87 as they are opposite angles and opposite angles are equal.
So y = 87/3
We can use the knowledge that angles in a straight line (in parallel line diagrams) will add up to 180. Therefore we do 180-87= 93. Now we know 3x=93 because just like the first example they are opposite angles. Now we know x=93/3.
(I didn’t have a calculator on me so you’ll have to work out the final result. Also I recommend looking into angles in parallel lines. I tried my best to explain so I hope you understand the jist of what I was trying to say.)

3 0

3 years ago

Read 2 more answers

Tickets to a concert cost $24 before a 5% fee is added.How much are the tickets with the fee?

vagabundo [1.1K]

Answer:

$25.20

Step-by-step explanation:

10%= 2.4 because you divide 24 by 10

So 5%= half 2.4= 1.2

24+1.2=25.20

5 0

3 years ago

Read 2 more answers

Assume that women's heights are normally distributed with a mean given by mu equals 63.2 in, and a standard deviation given by

JulijaS [17]

a. Your answer is correct.

b. Divide the given value of sigma by √n where n = sample size = 7. Then perform the same calculation you did for part a. The probabiilty is 0.4427.

8 0

3 years ago

Find the components of the vertical force Bold Upper FFequals=left angle 0 comma negative 10 right angle0,−10 in the directions

quester [9]

Solution :

Let $v_0$ be the unit vector in the direction parallel to the plane and let $F_1$ be the component of F in the direction of $v_0$ and $F_2$ be the component normal to $v_0$ .