How many solutions does this system of equations have?

A. No Solutions
B. 2
C. 1
D. An infinite number of solutions

How Many Solutions Does This System Of Equations Have?A. No SolutionsB. 2C. 1D. An Infinite Number Of

Answers

Answer 1
Answer: D) infinitely many solutions

===================================================

Explanation:

Let's solve the first equation for y

4x - 2y = 6

4x-6 = 2y

2y = 4x-6

y = (4x-6)/2

y = (4x/2) - (6/2)

y = 2x - 3

After doing so, we see that 4x-2y = 6 is equivalent to y = 2x-3

Therefore, the original system of equations is effectively listing the same equation twice (one has a different form compared to the other).

Both equations in this system produce the same graph, which leads to infinitely many solutions. All solutions are on the line y = 2x-3.

You can say that all solutions are in the form (x, 2x-3) where x is any real number you want.

-------------------------------

Here's another approach using substitution

4x - 2y = 6 ... start with the first equation

4x - 2( y ) = 6

4x - 2( 2x-3 ) = 6 .... replace y with 2x-3; ie plug in y = 2x-3

4x - 2(2x) - 2(-3) = 6

4x - 4x + 6 = 6

0x + 6 = 6

0 + 6 = 6

6 = 6

We get a true statement. The last equation is always true regardless of what we plug in for x, so this is another way to see how we get to infinitely many solutions.

Side note: the system is considered dependent since one equation depends on the other. The system is also consistent since it has at least one solution.


Related Questions

A rectangle has a length of 12 inches and a width of 8 inches. Lexi draws a scale factor of 0.5. What are the dimensions of the scale copy?

Answers

Answer:

6 inches and a width of 4 inches

Step-by-step explanation:

The growth of a tree in Andy's backyard has slowed down as the tree has continued to age. The heights of the tree over the past four years are: 10 feet, 11 feet, 12.1 feet, and 13.31 feet. Write a recursive formula for the height of the tree

Answers

Answer:

9.091(1.1^n)

Step-by-step explanation:

Given the height of a tree for the past 4 years given by the sequence;

10ft, 11ft, 12.1ft, 13.31ft...

We can see that the sequence is in geometric progression since they have a common ratio;

The nth term of a geometric progression is expressed as;

Tn = ar^n-1

a is the first term

r is the common ratio

Given

a = 10

r = 11/10 = 21.1/11 = 13.31/12.1 = 1.1

Substitute into the formula;

Tn = 10(1.1)^{n-1}

Tn = 10(1.1^n)/1.1

Tn = 9.091(1.1^n)

Hence the recursive formula for the height of the tree is expressed as  9.091(1.1^n) where n is the total number of tree.

What vector describes the transition depicted below !! Please help !!!

Answers

Answer:

vector v(4;-3)

Step-by-step explanation:

what is..
y=x+3 and y=-1/2x-3

Answers

Answer: (-4, -1)

Step-by-step explanation:

Francisco makes $11 per hour doing part time work on Saturdays. He spends $3 on transportation to and from work. The equation y = 11x - 3 gives his earnings y, after transportation costs, for working x hours. Complete the table of values for this situation.
x=2
x=3
x=4
x=5

Answers

Answer:

x=4

Step-by-step explanation:

Your salary is $65,788. If you work fifty 40-hour weeks in a year, what is your hourly wage?

Answers

Answer:

$31.63 per hour

Step-by-step explanation:

hope this helped,brainliest


Janiya received a 20% discount on the purchase of a $649 cell phone. What was the
amount of the discounT

Answers

Answer:

$129.80

Step-by-step explanation:

Discount:   .20 * 649 = 129.80

True or False:
1. If two half planes never intersect, then their boundary lines are parallel.
2. If the boundary lines of two half planes are parallel, then they have no solution area.

Answers

Answer:

1- true

2-true

Step-by-step explanation:

hope this helps have a good day

Answer:

1True

2True

hope this helps!

Find the slope of the line graphed below

Answers

7/3 rise over run hope it helps :)

Please help!! I have to find x and y!!

Answers

Answer:

X= 17.5

Step-by-step explanation:

the outside of the triangle always = 180

so you need to add up all the sides and equal to 180

5x+35+x+5+2x=180

add like terms

8x+40=180

get the x alone

x=17.5

Eric paints 8 rooms in 3 days for 600$

a. What is his painting rate in dollars per day?

b. How much does he receive on average for a room?

c. About how many rooms could Eric paint in 6 days?

Brainliest for correct answer

Answers

The answers are A200 b 75 c 16

qué son los ángulos?

Answers

Answer:

"what are angles"

Step-by-step explanation:

En la geometría euclidiana, un ángulo es la figura formada por dos rayos, llamados lados del ángulo, que comparten un punto final común, llamado vértice del ángulo. Los ángulos formados por dos rayos se encuentran en el plano que contiene los rayos. Los ángulos también se forman por la intersección de dos planos. Estos se llaman ángulos diedros

Factor 24x−20 using the GCF.

need it asap!

Answers

Answer:

The factor is 4.

Step-by-step explanation:

You can divide both 24 and 20 by 4, leaving you with 6x-5.

Highest common factor should be 4.

Given that,

The equation is 24x - 20.

Based on the above information, the calculation is as follows:

Here 24 and 20 should be divisible by 4

So,

= 4(6x - 5)

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I don't know how to solve this question.​

Answers

Answer:

P=Q=R

Step-by-step explanation:

Mark me as brainliest

If f(1)=7f(1)=7 and f(n)=f(n-1)+2f(n)=f(n−1)+2 then find the value of f(4)f(4).

Answers

Answer:

Step-by-step explanation: f1 =7

f2 = 5(7) + 2 = 37

f3 = 5(37) + 2 = 27

f4 = 5(9) + 2 = 47____

The value of f(4)f(4) f(1) = 7f(1) = 7 and f(n) = f(n-1) + 2f(n) = f(n−1) + 2 is,

121.

What is a function?

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given, f(1) = 7f(1) = 7 and f(n) = f(n-1) + 2f(n) = f(n−1) + 2.

By this pattern,

f(4)f(4) = [f(4 - 1) + 2f(4)][f(4 - 1) + 2f(4)].

f(4)f(4) =  [f(3) + 2f(4)][f(3) + 2f(4)].

f(4)f(4) =  [f(3) + 2(4)][f(3) + 2(4)].

f(4)f(4) =  [3 + 8][3 + 8].

f(4)f(4) =  [11][11].

f(4)f(4) =  121.

learn more about functions here :

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4600000000 in standard form

Answers

Answer:

four billion, six hundred million

Step-by-step explanation:

The diameter of a circle is 16 meters. What is the angle measure of an arc 6​ meters long?

Answers

Answer:

42.99° or approx 43°

Step-by-step explanation:

Diameter of circle d = 16 m

Lenght of arc l= 6 m

Let the angle measure of the arc be [tex] \theta [/tex]

By length of arc formula of a circle.

[tex]l = \frac{ \theta}{360 \degree} \times\pi d \\ \\ 6 = \frac{ \theta}{360 \degree} \times 3.14 \times \: 16 \\ \\ \theta = \frac{6 \times 360 \degree}{3.14 \times 16} \\ \\ \theta = \frac{2160\degree}{50.24} \\ \\ \theta = 42.9936306 \degree \\ \\ \theta = 42.99 \degree \approx \: 43 \degree[/tex]

The table and the graph show the relationship between the edge length, x, of a cube and its surface area, y. Is the relation a function?
Also weirdgamergirl7 if your watching this, ty for the answers <3

Answers

Answer:

Yes, the relationship between x and y is a non-linear function.

Step-by-step explanation:

Given the table

Edge Length, x            Surface Area, y

1                                             6

2                                            24

3                                            54

4                                             96

The table values clearly represent a function, because each input value has one and only one output value. i.e. there is no repetition of x values.

Also from the table values and the graph, it is clear that the function is not a linear function, because the graph is not a straight line. Also, In a cubic function, the highest power over the x variable(s) is 3. So, it is not a linear function.

Hence, we conclude that Yes, the relationship between x and y is a non-linear function.

Therefore, the 'last option' is correct.

Answer:

no it is non- linear

Step-by-step explanation:

30 points!!
Find the missing term to make each statement true
1. 18e + __ = 12e
2. __ - (-21x) = 21x
3. 90z + __ = 80z

Answers

Answer:

1. 18e + (-6e) = 12e

2. 0x - (-21x) = 21x

3. 90z + (-10z) = 80z

1. 18e + (-6e) = 12e

2. 0x - (-21x) = 21x

3. 90z + (-10z) = 80z

2. 112, 4
1. A(0,0), B(2, 2), C(-2, 0). D(1, -2)
2
3. P-3.3), (1.2). R(3.-3), S(1.-3).
4. D(2.

Answers

Answer: 1,3

Step-by-step explanation:

What is the y-intercept of
each graph? Explain.

Answers

The y intercept of the left graph is 2 and the y intercept for the right graph is -0.5. These are the points where the line cross the y-axis (the vertical axis)

Make & the subject of the
Formula
6x ta=5(x+t)

What is the answer please

Answers

Answer is x = 5t-a

6x+a = 5(x+t) Expand the bracket
6x+a = 5x+5t Subtract the least x’s (so 5x)
x+a = 5t Subtract a to make x the subject
x = 5t-a

Answer:

x  = 5t - a

Step-by-step explanation:

The problem deals with making a variable the subject of the formula in the expression.

 Given expression:

            6x + a = 5(x + t)

  We are to make x the subject of the formula in the expression

   

Solution:

           6x + a  = 5(x+t)

On the right hand side, expand the parentheses and distribute the term outside;

          6x + a  = 5x + 5t

   Bring the term desired to be the subject to one side by adding (-5x) to both sides;

     6x + (-5x) + a = 5x + (-5x) + 5t

           x + a  = 5t

  Now add (-a) to both sides

         x + a + (-a) = 5t + (-a)

          x  = 5t - a

TRANSFORMATIONSS PLS HELP DUE IN AN HOUR

Answers

Answer:

transformation across the x axis

Answer:

Reflection over the X-axis

Step-by-step explanation:

That's the only thing I can think of. Can you list the choices, though? It could be a reflection followed by a translation...

Help ASAP!
Question:
Identify the function that reflects f(x) = 14x3 − 7x2 + 6 across the y-axis and shifts it 6 units up.
Answer:
h(x) = 14x3 + 7x2 + 12
h(x) = −14x3 − 7x2 + 12
h(x) = −14x3 − 7x2
h(x) = 14x3 − 7x2

Answers

Answer: there's no answer, the correct answer is f(x) = -14x3 + 7x2

Step-by-step explanation:

1. f(x) = 14x3 − 7x2 + 6

2. reflection over y-axis : f(x) = -14x3 + 7x2 - 6

3. shift 6 units up : f(x) = -14x3 + 7x2 - 6 + 6

4. f(x) = -14x3 + 7x2

The correct function after reflection across the y-axis and shifts it 6 units up is,

⇒ h (x) = - 14x³ - 7x² + 12

What is Function?

A relation between a set of inputs having one output each is called a function.

We have to given that;

The function is,

⇒ f (x) = 14x³ - 7x² + 6

Now, After reflection across the y-axis we get;

⇒ f (x) = f (- x)

⇒ f (-x) = 14 (-x)³ - 7 (-x)² + 6

⇒ f (-x) = - 14x³ - 7x² + 6

And, After shifts it 6 units up, we get;

⇒ f (x) = f (x) + 6

Hence, We get the value of function is,

⇒ h (x) = - 14x³ - 7x² + 6 + 6

⇒ h (x) = - 14x³ - 7x² + 12

Learn more about the function visit:

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pls answer this i will dir

Answers

Answer:

59 cuz it's an isosceles triangle (two sides and two angle are equal)

A grocery store is selling peaches for $0.98 per pound. Is this a function or Not function

Answers

Answer:

This is a function. Use y=mx+b equation

Step-by-step explanation:

To find the x and y values, simply plug in 0.98 to m. For every pound of peaches, you pay $0.98. The equation would be y=0.98x, where x is the number of pounds of peaches and y is the total cost.

EASY PLEASE HELP PLEASE HELP 15 POINTS...PLEASE HELP

Answers

Answer:

if im correct the y intercept if -1

Step-by-step explanation:

thats where the line crosses the y axes

Answer:

-1

Step-by-step explanation:

The line on the graph goes through the y axis at point -1

4. On the day Alex was born, his father invested $5000 in an account with a 1.2% annual growth rate.
Answer the questions below.
(a) Write a function, A(t), that represents the value
of this investment t years after Alex's birth.
(b) Use your equation to determine how much the
investment will be worth when Alexander turns
21

Answers

Answer and Step-by-step explanation:

A)    A(t) = 5000(1 + 0.012)t

B)    A(t) = 106260

A) 5000 is the initial amount, 1 + 0.012 is the interest rate, and t represents the years.

B) When we plug 21 into the equation,  we get 106260.

I hope this helps!

Part A
The art club had an election to select a president.
75% of the 60 members of the club voted in the election,
How many members voted?
Answer:
members.
Part B.
How many members did not vote?
Answer:

Answers

no of members who voted=

75/100x60=45members

no of members who did not vote=

60-45=15 members

I NEED HELP!!!!
(3.2 x 10^4)(1.4 x 10^2)

Evaluate each expression Express result in scientific notation

I need help learning to do this IM GIVING EXTRA POINTS!!!

Answers

Step-by-step explanation:

So Scientific Notation is like this.

Ya got a big number that has of 0s . Let's just throw out 69,000,000,000,000

You take the other numbers that arent 0s. Take the first number and put a "." in between it and the second number. So, in this case, you have 6.9, like this.

You then count the number of 0s and +1. So in this case, you'll have 12+1. Which is 13.

You then take the 6.9 and note it with a *10. You then take the 13 and put it on the 10 as an exponent. So in the end youll have 6.9*10^13.

Hopefully, this helps.

With love,

A G 4 2

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