2x-y=4
-2x+y=7
is there a solution

Answers

Answer 1

[tex] \text{Given : 2x - y = 4 and x + 2y = 7}[/tex]

[tex] \text{Solution : according to the question here we are provided with} \\ \text{two equations separately. So, let's name them as eq(1) and eq(2).} \\ \text{ The rest is followed as we continue to get to our goal} \\ \\ \sf {1}^{st} \: equation : \\ \quad\dashrightarrow \frak{2x - y = 4} \\ \\ \quad \dashrightarrow \frak{ \red{x = \frac{y + 4}{2} }} \qquad \sf ...eq(1) \\ \rm{ now \: \: as \:per \: our \: plan \: we \: need \: to \: get \: eq(2) } \\ \\ \sf{ {2}^{nd} \:equation} : \\ \quad\dashrightarrow \frak{ x + 2y = 7} \\ \\ \quad\dashrightarrow \frak{ \red{y = \frac{7 - x}{2}}} \qquad \sf ...eq(2) \\ \\ \text{Now, finding x and y} \\ \\ \underline{ \frak{Finding \: x}}\\ \\ \quad \hookrightarrow \frak{x = \frac{y + 4}{2}} \\ \\ \quad \hookrightarrow \frak{2x = \frac{7 - x}{2} + 4} \\ \\ \quad \hookrightarrow \frak{2x = \frac{7 - x + 8}{2}} \\ \\ \quad \hookrightarrow \frak{2x = \frac{1 - x}{2}} \\ \\\quad \hookrightarrow \frak{4x = 1 - x} \\ \\ \quad \hookrightarrow \frak{5x = 1} \\ \\\quad \star \qquad \underline{ \boxed{ \green{ \frak{x = \frac{1}{5}}}}} \\ \\ \underline{ \frak{Finding \: y}} \\ \\ \quad \hookrightarrow \frak{y = \frac{7 - x}{2}} \\ \\ \hookrightarrow \frak{2y = 7 - \frac{1}{5} } \\ \\ \hookrightarrow \frak{2y = \frac{35 - 1}{5} } \\ \\ \hookrightarrow \frak{2y = \frac{34}{5}} \\ \\ \hookrightarrow \frak{y = \frac{34}{5} \times \frac{1}{2}} \\ \\ \hookrightarrow \frak{y = \frac{17}{5} } \\ \\ \star \qquad \underline{ \boxed{ \frak{ \green{y = 3 \frac{2}{5} }}}}[/tex]


Related Questions

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:

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

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


4. What are the zeroes
of y = x^2 + 2x – 8? (1 point)
-4, 2
4, 2
-4,2
4, 2

Answers

Answer:

-4,2

Step-by-step explanation:

(x-2) (x+4)=0

x-2=0

x=2

x+4=0

x= -4

Answer:

x=-4, x=2

Step-by-step explanation:

Whenever a question asks you to find the zeros of a quadratic equation, they are essentially asking you to find the x-intercepts. To find the x-intercepts, you simply need to equate y to zero and solve for x.

There are two main ways to find the intercepts - by the quadratic formula and factoring. I will demonstrate both below.

When factoring, a popular method is the diamond box method. First, make an x on your paper. In the top nook of the x, write the product of a and c in y=ax^2 +bx +c. Here, it is -8*1=-8. In the bottom nook, write the b value. Here it is 2. Find two numbers that multiply to ac or -8 and add up to b or 2 and write them in the side nooks. In this problem, they are 4 and -2 (4*-2=-8 and 4+(-2)=2). Then, make a box. On the top left corner, write the first term (here it is x^2) and on the bottom right corner write the constant term (here it is -8) and write the two values you found earlier in the remaining boxes. Now, find values that multiply to each of the respective terms. Sorry, this sounds super confusing, I have included a picture below of what the result should look like. Once you have it factored, make y equal to zero and solve for both x's. You should get x=2 and x=-4. Keep in mind, sometimes, a problem might not be factorable. If it isn't, you have to use the method below.

Another popular way to find the roots is the quadratic formula. I have included a picture of it below. All you have to do is substitute the coefficients in and solve for x. You should get two solutions in this scenario.

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.

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:

The perimeter of a rectangle is 40 cm. The length is 14 cm.
Let x = width of the rectangle.
Ravi says he can find the width using the equation 2(x + 14) = 40.
Fran says she can find the width using the equation 2x + 28 = 40.
Answer the questions to solve the equations and to compare the steps and solutions.
1. Which of these is the most helpful first step for solving Ravi's equation, 2(x + 14) = 40?
Circle the best answer.
Add 14 to both sides
Subtract 14 from both sides
Divide both sides by 2
Multiply both sides by 2














2. What would your next step be?

Write your answer in the space below.














3. Solve Ravi's equation, 2(x + 14) = 40, to find the width of the rectangle. Show your work.

Write your answer in the space below.2(x +14) = 40 (use the distributive property)
2x + 28 = 40 (solve exactly like you did for Fran)
2x = 12
x = 6















4. Which of these is the most helpful first step for solving Fran's equation, 2x + 28 = 40?
Circle the best answer.
Multiply both sides by 2
Subtract 28 from both sides
Divide both sides by 2
Add 28 to both sides














5. What would your next step be?

Write your answer in the space below.














6. Solve Fran's equation, 2x + 28 = 40, to find the width of the rectangle. Show your work.

Write your answer in the space below.














7. The two equations have different solution steps. Do they have the same solution? Use the distributive property to show why this answer makes sense.

Write your answer in the space below

Answers

Answer:

Below.

Step-by-step explanation:

1. Divide both sides by 2.

2. After dividing both sides by we would have:

x + 14 = 20

The next step would be

Subtract 14 from both sides.

3. 2(x + 14) = 40

x + 14 = 20

x = 20 - 14

x = 6.

2x + 28 = 40

2x = 40 - 28

2x = 12

x = 6.

I need help on 26 please and thank you

Answers

Answer:

your answer is 1.65 or E :)


6) Convert 2pie/3 to degrees
A) 30°
B) 60°
120°
D) 240°

Answers

it would be c . 1.20

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.

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]

Which figure in the drawing best represents a dilation of figure A with a scale factor of 1.5?
A.r
b.q
c.s
d.t​

Answers

I’m pretty sure it’s b

A diameter of a circle measures 58cm. What is the length of its radius

Answers

Answer:

29cm

Step-by-step explanation:

a radius is half of a diameter so half of 58cm  is 29cm.

i hope this helps have a good day

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.

theres the picture i dont know how to write it out.​

Answers

Answer:

x > -2

Step-by-step explanation:

As the circle in the number line is not filled, it will not include -2 and as the number line starts from -2 and goes right it will be x > -2.

Hope this 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])

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.

what is the product of... see attachment below

Answers

The answer is -7 (option A)

Steps are in the attachment.

_________

Hope it helps ✌

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

Answer Asap!
<3 <3 <3
Thx

Answers

Answer:

the answer is 15/17

because cosine=b/h=UV/UW=15/17

4. Algebra If in one year a city
recorded a total of 97 rainy days,
how many of the days did it NOT
rain? Write and solve an equation.

Answers

Answer:

268.25

Step-by-step explanation:

by using the fact that one year is 365.25 days, we can subtract our 365.25 by our 97 to get 268.25, written in the equation of 365.25-97=268.25

*edit, messed up how long a year was, corrected my issue, answer & equation.

Answer:

Step-by-step explanation:

How many did not rain is 268 because if you take away 97 from 365 ofcourse it will be 268 you’re welcome

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

What did she do wrong? What can she do to prevent this?

Answers

Answer:

y = 8x + 14  (8x is WRONG)

This is how it is supposed to be

y - 2 = 6x + 12

y = 6x + 14

She must combine like terms, not unlike terms

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

Answers

x=31/14

Step-by-step explanation:

I did the second one btw

Solve the simultaneous equation


3x-4y=11
9x+2y=5

Answers

Answer:

I assume you are looking for the x and y values of the two equations? if not message me!

y=–2

x=1

Step-by-step explanation:

Multiply the first/top tearm by –3 so we can "get rid of" the X's with the addition of both equations. we are then left with: 14y=-28

We can now divide both sides by 14 to get y by itself so we are left with: y=–2

plugging our y value back into the first equation we get: 3x+8=11. we subtract 8 from both side and are left with: 3x=3. dividing both side by 3 we can get x by itself and are left with: x=1

To check, we plug x and y both into the first equation we get: 3+8=11 (which it does). Or we can plug both of them into the second equation and we get:9-4=5 (which it does)

Answer:

Below in bold.

Step-by-step explanation:

3x-4y=11

9x+2y=5

Multiply the first equation by 3:

9x - 12y = 33

Subtract the above from the second equation:

2y - (-12y) = 5 - 33

14y = -28

y = -2.

Now plug y = -2into the first equation:

3x - 4(-2) = 11

3x = 11 - 8 = 3

x= 1.

plssss help picture down below

Answers

Answer:

it is (-4,1)

Step-by-step explanation:

Hope this helps:)

a canine's body temperature is considered to be normal if it is 101 degrees Fahrenheit with an absolute deviation of 1.5 degrees Fahrenheit.
A. write an absolute value inequality that represents the normal temperature range. B.solve the inequality. what is the normal temperature range?

Answers

Answer:

Please I don't understand the question or maybe I'm too young for the question I'm so sorry

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

If Ram had 5 apples in house , now calculate the number of apple's in his neighbours house . ​

Answers

Answer:

Ram's neighbors probably had more apples than Ram.

Hence, number of apples in the neighbor's house is equal to [tex] \geqslant 5[/tex].

Step-by-step explanation:

Hello bro ufff.... Finally found u xD-,-

The lenght of a rectangle exceeds it width by 2cm. If area of the rectangle is 80 cm The lenght of the rectangle is ?​

Answers

Answer:

[tex]x4 - (9x5)[/tex]

yan npo wag puro brainly

Answer:

The answer is l =40cm

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