1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Bingel [31]
3 years ago
12

Two systems of equations are shown below: System A System B 3x + 2y = 3 −x − 14y = 1 −2x − 8y = −1 −2x − 8y = −1 Which of the fo

llowing statements is correct about the two systems of equations? The value of x for System B will be one−third of the value of x for System A because the coefficient of x in the first equation of System B is one third times the coefficient of x in the first equation of System A. The value of x for System A will be equal to the value of y for System B because the first equation of System B is obtained by adding −4 to the first equation of System A and the second equations are identical. They will have the same solution because they represent the same lines when plotted on the coordinate axes. They will have the same solution because the first equation of System B is obtained by adding the first equation of System A to 2 times the second equation of System A.
Mathematics
2 answers:
Sauron [17]3 years ago
6 0

The two linear equations represented in system A as :

3 x + 2 y =3   -------(1)

- 2 x - 8 y = -1  ------(2)

(1) × 2 + (2) × 3 gives

⇒ 6 x + 4 y - 6 x - 24 y = 6 -3

⇒ - 20 y = 3

⇒ y = \frac{-3}{20}

Putting the value of y in equation (1), we get

3 x  - \frac{6}{20}=3\\\\ 3 x= \frac{66}{20} \\\\ x=\frac{11}{10}

Two linear equation represented in system B is:

3.   -x - 14 y =1

4.   - 2 x - 8 y = -1

-2 ×Equation (3) + Equation (4)=

2 x +28 y- 2 x - 8 y= -2 -1

⇒ 20 y = -3

⇒y =\frac{-3}{20}

Putting the value of y in equation (3),we get

-x + \frac{42}{20}=1 \\\\ x=\frac{22}{20}=\frac{11}{10}

As Two system , that is system (A) and System (B) has same solution.

By looking at all the options , i found that Option (D) is correct. The two system will have the same solution because the first equation of System B is obtained by adding the first equation of System A to 2 times the second equation of System A.

IRINA_888 [86]3 years ago
5 0

Answer:

(D)

Step-by-step explanation:

Two linear equations by system A is given as:

3x+2y=3           (1)

-2x-8y=-1          (2)

Multiply equation (1) with 2 and equation (2) with 3 and then adding, we get

6x+4 y-6x-24y=6-3

-20y=3

y=\frac{-3}{20}

Putting the value of y in equation (1), we get

3x-\frac{6}{20}=3

3x=\frac{66}{20}

x=\frac{11}{10}

Two linear equations by system B is given as:

-x-14y=1       (3)

-2x-8y=-1     (4)

Multiply equation (3) with -2 and adding equation (4), we get

2x+28y-2x-8y=-2-1

20y=-3

y=\frac{-3}{20}

Putting the value of y in equation (3),we get

-x+\frac{42}{20}=1

x=\frac{11}{10}

As Two system , that is system (A) and System (B) has same solution.

Thus,  Option (D) is correct. The two system will have the same solution because the first equation of System B is obtained by adding the first equation of System A to 2 times the second equation of System A.

You might be interested in
Solve for y: 1/3y+4=16
katovenus [111]

Hey there! I'm happy to help!

We want to isolate y on one side of the equation to see what it equals. To do this, we use inverse operations to cancel out numbers on the y side and find the correct value.

1/3y+4=16

We subtract 4 from both sides, canceling out the +4 on the right but keeping the same y-value by doing the same to the other side.

1/3y=12

We divide both sides by 1/3 (which is multiplying both sides by 3) which will cancel out the 1/3 and tell us what y is equal to.

y=36

Now you know how to solve basic equations! Have a wonderful day! :D

4 0
3 years ago
Read 2 more answers
“40% of what number is 34?”
zepelin [54]
85. i provided a picture just incase you needed your work shown.

4 0
3 years ago
Read 2 more answers
Simplify the expression3х + 8 + 13x =
leva [86]

Answer:

8(2x+1)

Step-by-step explanation:

First we add

16x + 8

Next take GCF

8(2x+1)

6 0
3 years ago
The average of 5 quiz grades is 10. When the lowest grade is dropped and the new average is calculated, it turns out to be 11. W
V125BC [204]

Answer:

The score of the dropped grade is 6

Step-by-step explanation:

To find the average of a set of numbers you need to add all the numbers and divide by how many numbers there are. The problem wants you to solve it in reverse. Let put this into an algebraic equation with a, b, c, d, and e being the variables of the test scores

(a+b+c+d+e)/5=10

Then we can multiply both sides by 5 and get

a+b+c+d+e=50

Lets assume that c is the lowest test score. To calculate the average of that we get

a+b+d+e/4=11

Doing the same thing, we know that a+b+d+e=44

Now compare the two:

a+b+c+d+e=50

a+b+d+e=44

We can now know that c=50-44=6

So, 6 is the score of the dropped quiz. Hope that helped!

4 0
3 years ago
Determine which of the lines, if any, are parallel or perpendicular. Explain.
hodyreva [135]
Answer:
line a and b are parallel
line c is not perpendicular because it is not 3

step-by-step explanation:
if the slope is the same it is parallel
if the slope is the complete opposite it is perpendicular
lines a and b are parallel with a slope of -1/3
(0, 5) (3, 4)
m = 4 - 5 / 3 - 0
m = -1 / 3
m = -1/3
(-1, 1) (2, 0)
m = 0 - 1 / 2 + 1
m = -1 / 3
m = -1/3
line c is perpendicular to lines a and b the slope is
(0, 0) (2, 5)
m = 5 - 0 / 2 - 0
m = 5/2
2.5
8 0
3 years ago
Other questions:
  • The function f(x) is continous on the interval (-3, 4). If we know that f(-1) = 4 and f(3) = 7, what can we say about the output
    12·1 answer
  • Angle A and B are complementary<br> What is the value of x?
    10·2 answers
  • A line segment AB has the coordinates A (2,3) AND B ( 8,11) answer the following questions (1) What is the slope of AB? (2) What
    9·1 answer
  • help I’ll give you brainliest
    5·2 answers
  • 30 POINTS NO CAP PUT REALL STUFF
    11·1 answer
  • Calculate the cash flow to stockholders
    8·1 answer
  • FRIEND ME PLZ IM NICE
    7·2 answers
  • I will give brainlyist to the first right answer
    6·2 answers
  • Solve the equation.<br><br> 3(x−9)=30
    8·1 answer
  • Alexa's friends got her a skydiving lesson for her birthday.
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!