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
kkurt [141]
3 years ago
9

Johanna wrote the system of equations. 4 x - 3 y = 1, 5 x + 4 y = 9. If the second equation is multiplied by 4, what should the

first equation be multiplied by to eliminate the x-variable by addition?
Mathematics
2 answers:
Andru [333]3 years ago
7 0

Answer:

To eliminate x

We multiply Equation 1 by -5

The results are

X = 1

Y= 1

Step-by-step explanation:

4 x - 3 y = 1. .............Equation 1

5 x + 4 y = 9........... Equation 2

If equation 2 is multiplied by 4

4*(5x + 4y = 9)

20x + 16y = 36...... Equation 3

To eliminate x

We multiply Equation 1 by -5

-5*(4 x - 3 y = 1. )

-20x +15y = -5 ..... Equation 4

So we add Equation 3 and Equation 4

31y = 31

Y = 1

Substitute y into Equation 1

4x = 4

X = 1

polet [3.4K]3 years ago
4 0

Answer:

The first equation must be multiplied by -5 to eliminate x variable by addition

Step-by-step explanation:

4 x - 3 y = 1 (1)

5 x + 4 y = 9 (2)

If the second equation is multiplied by 4

5x+4y=9. ×4

We have,

20x+16y=36 (3)

The first equation should be multiplied by -5 to eliminate x variable by addition

4x-3y=1 × -5

We have

-20x+15y=-5 (4)

Add equation (3) and (4) to eliminate x variable

20x+16y=36

-20x+15y=-5

31y=31

Divide both sides by 31

y=1

Substitute y=1 into equation (1)

4 x - 3 y = 1

4x-3(1)=1

4x-3=1

4x=1+3

4x=4

Divide both sides by 4

x=1

You might be interested in
Karl is building a rectangular garden bed. The length is 6 feet. She has 20 feet of boards to make the sides. Write and solve an
natali 33 [55]

Answer:

The width of the garden bed must be less than or equal to 4 feet.

w\leq4

Explanation:

Given that;

She has 20 feet of boards to make the sides.

The perimeter of the garden bed must not be more than 20 feet

\begin{gathered} P=2l+2w\leq20 \\ 2l+2w\leq20 \end{gathered}

Given;

The length is 6 feet;

l=6

To get the inequality for the width w, let us substitute the value of the length into the inequality above and simplify;

\begin{gathered} 2l+2w\leq20 \\ 2(6)+2w\leq20 \\ 12+2w\leq20 \\ 2w\leq20-12 \\ 2w\leq8 \\ \frac{2w}{2}\leq\frac{8}{2} \\ w\leq4 \end{gathered}

Therefore, the width of the garden bed must be less than or equal to 4 feet.

w\leq4

8 0
1 year ago
What is the area of the figure? A) 18 in2 B) 24 in2 C) 30 in2 D) 36 in2
Annette [7]
Hello!

You need to separate this into two rectangles and add their areas together

first rectangle

3 * 6 = 18

rectangle 2

3 * 2 = 6

18 + 6 = 24

the answer is 24in squared


5 0
3 years ago
Read 2 more answers
Question: why are the y-intercept and slope of the graphed line? I need help asap thanks! It’s for a test
damaskus [11]
Your answer should be J.
6 0
2 years ago
If your barn is 100 feet by 50 feet, how many square feet do you have in your barn? Type in your answer.
zavuch27 [327]

Answer: 5,000 square feet

Step-by-step explanation:

50 feet multiplying by 100 feet equal to 5,000 sq ft.

7 0
3 years ago
Read 2 more answers
Each of these extreme value problems has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to f
tino4ka555 [31]

Answer:

The minimum value of the given function is f(0) = 0

Step-by-step explanation:

Explanation:-

Extreme value :-  f(a, b) is said to be an extreme value of given function 'f' , if it is a maximum or minimum value.

i) the necessary and sufficient condition for f(x)  to have a maximum or minimum at given point.

ii)  find first derivative f^{l} (x) and equating zero

iii) solve and find 'x' values

iv) Find second derivative f^{ll}(x) >0 then find the minimum value at x=a

v) Find second derivative f^{ll}(x) then find the maximum value at x=a

Problem:-

Given function is f(x) = log ( x^2 +1)

<u>step1:</u>- find first derivative f^{l} (x) and equating zero

  f^{l}(x) = \frac{1}{x^2+1} \frac{d}{dx}(x^2+1)

f^{l}(x) = \frac{1}{x^2+1} (2x)  ……………(1)

f^{l}(x) = \frac{1}{x^2+1} (2x)=0

the point is x=0

<u>step2:-</u>

Again differentiating with respective to 'x', we get

f^{ll}(x)=\frac{x^2+1(2)-2x(2x)}{(x^2+1)^2}

on simplification , we get

f^{ll}(x) = \frac{-2x^2+2}{(x^2+1)^2}

put x= 0 we get f^{ll}(0) = \frac{2}{(1)^2}   > 0

f^{ll}(x) >0 then find the minimum value at x=0

<u>Final answer</u>:-

The minimum value of the given function is f(0) = 0

5 0
3 years ago
Other questions:
  • Which properties are present in a table that represents an exponential function in the form y=bx
    7·1 answer
  • What is 9x-2?????????????
    8·1 answer
  • The coefficient of the product of (-5xy2) and (-4x2y) is
    10·1 answer
  • Please answer these questions ....please....
    14·1 answer
  • Solve this system of linear equations using elimination:<br><br> 5x+2y=34<br><br> 3x+3y=33
    9·2 answers
  • Katherine is conducting an experiment with bacteria where she cools the temperature of one bacteria to -51°C and the other bacte
    12·1 answer
  • PLEASEEE EXPLAIN
    8·1 answer
  • Pls answer quickly
    6·2 answers
  • 2x2 +5x+8<br> Given x 3-2, the expression<br> x+2.<br> is equivalent to
    6·1 answer
  • I need help what's the answer ​
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!