How can you determine the number of solutions of a system by looking at the equationz

Answers

Answer 1

Answer:

Look at the variables and numbers in the equation, and what it equals

Step-by-step explanation:

Expressions that are the exact same have infinite solutions

[tex]5x+3=5x+3[/tex]

Expressions that are different have 1 solution

[tex]6x+7=5x-2[/tex]

Expressions that are the same with different operands have no solution

[tex]5x-3=5x+3[/tex]

Answer 2

Explanation:

The short of it is that when the equations are in the same form, if one equation is the same as or a multiple of the other, there are infinite solutions. If one equation is the same as or a multiple of the other, except for the constant terms, there are no solutions. Otherwise, there is one solution.

Example:

If one equation is x +2y = 3, then you can consider the other equation:

  3x +6y = 9 . . . . 3 times the first equation: infinite solutions

  3x +6y = 6 . . . . 3 times the first equation; constants differ: no solutions

  3x -6y = 9 . . . .  not a multiple of the first equation: one solution

_____

Here's a more formal method.

Put both equations of the linear system of two equations into general form:

  ax +by +c = 0

  dx +ey +g = 0

Perform the following arithmetic:

  p = ae -db . . . . . this is called the system "determinant"

  q = bg -ec

  r = cd -ga

If p = q = r = 0, the equations describe the same line, so there are infinite solutions.

If p = 0 and either of q ≠ 0 or r ≠ 0, the equations describe parallel lines, so there are no solutions.

If p ≠ 0, there is one solution: (x, y) = (q/p, r/p).

_____

Additional comment

This method can always be used to find the solution to a system that is known to have one solution. It often requires fewer arithmetic operations than other solution methods. It is a variation of what is sometimes called the "cross multiplication method."


Related Questions

What is -45+30-(-60)=?

Answers

Answer:

45

Step-by-step explanation:

-45 + 30 gives you -15. When subtractinf a negative number, it actually turning into addition/positive. This changes it into -15 + 60, which is 45.

Answer: 45

Step-by-step explanation:

-45+30-(-60)=
First, times the negative 60 with the negative outside the parenthesis.

-45+30+60

60+30=90

90-45=45

Answer: 45

4. Find the center and radius of the circle with equation x2 + y2-2x + 4y -
11 = 0

Answers

Answer:

(1 , -2) and r = 4

Step-by-step explanation:

x² + y² - 2x + 4y - 11 = 0

x² - 2x + 1 - 1 + y² + 4y + 4 - 4 - 11 = 0

(x - 1)² - 1 + (y + 2)² - 4 - 11 = 0

(x - 1)² + (y + 2)² = 16

We know equation of circle is of the form

(x - h)² + (y - k)² = r²

So, center is (1 , -2) and radius is 4

HELPPPP
In the diagram to the​ right, GKNM~VRPT.
Find the value of x. Give the scale factor of the left polygon to the right polygon.

Answers

Answer: Sorry, I had a different problem than you so this answer isn't correct for the OP but hopefully it shows you how to solve.

x=27/5

The scale factor is 7:3

Step-by-step explanation:

f(x) = 3x^2 - 9x + 2
What's the axis of symmetry?
What's the coordinate of the vertex?

Answers

Answer:

1) Axis of symmetry = [tex]\frac{3}{2}[/tex]

2) Vertex form = [tex]y=3(x-\frac{3}{2} )^{2} -\frac{19}{4}[/tex]

Rewrite in vertex form and use this form to find the vertex (h,k).

[tex](\frac{3}{2} ,-\frac{19}{4} )[/tex] (coordinates of the vertex)

Step-by-step explanation:

Vocabulary:

Axis of symmetry

- A line that passes through a figure in such a way that the part of the figure on one side of the line is a mirror reflection of the part on the other side of the line.

Vertex

- The point on an angle where the two sides intersect.

Answer  

Thats the answer below!

Step-by-step explanation:

Pleas I really really need help

Answers

Answer:

3.5 gallons of gas

Step-by-step explanation:

If m = miles

And the equation is m = 40g

Then: 140 = 40g

40g/40 = 140/40

g = 3.5 gallons of gas.

The car used "3.5" gallons of gas.

the numbers of motor vehicle fatalities in the united states for the years

Answers

For 2016 specifically, National Highway Traffic Safety Administration (NHTSA) data shows 37,461 people were killed in 34,436 motor vehicle crashes, an average of 102 per day. In 2010, there were an estimated 5,419,000 crashes, 30,296 deadly, killing 32,999, and injuring 2,239,000.

A set of mathematics exam scores are normally distributed with a mean of 80.280.280, point, 2 points and a standard deviation of 444 points. What proportion of exam scores are between 828282 and 85.685.685, point, 6 points? You may round your answer to four decimal places.

Answers

Answer:

0.2379

lmk if im wrong :)

Approximately 0.2200 or 22.00% of the exam scores are between 82.2 and 85.6.

To find the proportion of exam scores between 82.2 and 85.6, we need to calculate the z-scores for both values and then use the standard normal distribution table (also known as the z-table) to find the proportion.

The z-score for a value x in a normal distribution with mean μ and standard deviation σ is given by the formula:

z = (x - μ) / σ

where x is the value, μ is the mean, and σ is the standard deviation.

Let's calculate the z-scores:

For x = 82.2:

z₁ = (82.2 - 80.2) / 4 = 2 / 4 = 0.5

For x = 85.6:

z₂ = (85.6 - 80.2) / 4 = 5.4 / 4 = 1.35

Now, we can find the proportion of scores between these z-scores using the z-table. The table gives us the cumulative probability up to a certain z-score.

From the z-table, the cumulative probability for z₁ = 0.5 is approximately 0.6915, and the cumulative probability for z₂ = 1.35 is approximately 0.9115.

Now, we can find the proportion of scores between these two z-scores:

Proportion = P(0.5 ≤ z ≤ 1.35)

= P(z ≤ 1.35) - P(z ≤ 0.5)

= 0.9115 - 0.6915

≈ 0.2200

So, approximately 0.2200 or 22.00% of the exam scores are between 82.2 and 85.6.

Learn more about z-scores click;

https://brainly.com/question/32011298

#SPJ3

Please find the value of X!​

Answers

Answer:

or,180=3x

or,x=180+3

or,x=183 answer

Answer:

54

Step-by-step explanation:

there are 2 ways

(180 - 18) ÷ 3 = 54

(360-18-18) ÷ 6 = 54

same answer

PLEASE HELP ME QUICKKK, FIRST CORRECT PERSON GETS BRAINLIEST​

Answers

Answer:

answer d and e

Step-by-step explanation:

First, you need to figure out the radius of B.

As radius of A is 6 in, 20% of 6in would be 1.2in. So total radius of B = 6+1.2 = 7.2

Now you get the radius of B, calculate th area of B using the formula πr^2.

= π(7.2)^2 = 162.86 = area of B

Now, all answers except D and E is smaller than B. So, the answer would be D and E.

Answer:

  A, E

Step-by-step explanation:

The radius of Circle B is 20% greater than 6 inches, so is ...

  r = (6 in)(1 +20%) = 1.2×6 in = 7.2 in

The area of Circle B is ...

  A = πr²

  A = π(7.2 in)² ≈ 162.86 in²

The offered answer choices (and the area of Circle B) in order from least to greatest are ...

  [B]51.84, [C]113.04, [F]148.49, [D]162.78,

  (circle B)162.86,

  [A}189.31, [E]203.15

Choices A and E are greater than Circle B's area.

are -8h - 3.5 and -0.5(16h - 7) equalivalent expressions? ​

Answers

Answer: Yes because they both have the same total

Step-by-step explanation:

In Figure 1, the area of square A is 9 square units, the area of square B is 16 square units, and the area of square C is 25 square units.


In Figure 2, the area of square D is 36 square units and the area of square E is 64 square units.


What is the area of square F in Figure 2?

A.

110 square units

B.

100 square units

C.

90 square units

D.

80 square units

Answers

Answer:

b) 100 square units as 36 add 64 is 100

please help. its on zearn name the coordinates of each shape

Answers

Answer:

circle: 2, 1/2

square: 1 1/2, 3 1/2

triangle: 0, 4 1/2

Answer:

Square X-coordinate: 1 and 1/2

Square Y-coordinate: 3 and 1/2

Triangle X-coordinate: 0

Triangle Y-coordinate: 4 and 1/2

Step-by-step explanation:

A hardware store stocks 85 reels of garden hose, each
containing 30 m of hose. How many kilometres of
garden hose are stocked by the store?

Answers

It's given that, the hardware store stocks 85 reels of garden hose. Each of them measure to be of 30 m.

Total length of hoses = 85 × 30

= 2550 m

= 2.550 km

= 2.5 km (approx.)

2.5 km of garden hose are stocked by the store.

Find the area of the shaded region.

Answers

Answer:

[tex] \boxed{ \tt\longrightarrow \: Area \: Of \: Shaded \: region \: =\boxed{ \tt 39 \: in²}}[/tex]

Step-by-step explanation:

Given:

The Dimensions of Parallelogram are 12 in.(Base) and 7 in.(Height)

And,

The Dimensions of Rectangle are 9 in.(Length) and 5 in.(Breadth).

To Find:

The Area of Shaded region

Solution:

When the dimensions of parallelogram and the dimensions of rectangle are given, we need to find the Shaded region using this formula:

[tex] \boxed{\tt \longrightarrow Area = (Parallelogram - Rectangle)}[/tex]

We know that the formula of Parallelogram is base*height[h] and the formula of rectangle is length*breadth[l*b] .

[tex] \tt\longrightarrow \: Area =B×h-l×b [/tex]

Put their values accordingly:

[tex]\longrightarrow \tt Area = (12 \times 7 - 9 \times 5)in {}^{2} [/tex]

Simplify it.

[Follow BODMAS Rule strictly while simplifying]

[tex] \tt\longrightarrow \: Area = (84 - 45 ) in {}^{2} [/tex]

[tex] \tt\longrightarrow \: Area = 39 \: {in}^{2} [/tex]

Hence, the Area of Shaded region would be 39 in² or 39 sq. in. .

[tex] \rule{225pt}{2pt}[/tex]

I hope this helps!

Solve the following system of equations using the elimination method. 8x – 5y = 5 –8x – 6y = 6 Question 3 options: A) (0,1) B) (0,–1) C) (2,–3) D) (–2,3)

Answers

Answer:

B: x = 0, y = -1

Step-by-step explanation: Hope it Helps!

Answer:

(0,-1)

Step-by-step explanation:

8x – 5y = 5

–8x – 6y = 6

-11y = 11

/-11 /-11

y = -1

8x – 5y = 5

8x - 5(-1) = 5

8x - (-5) = 5

8x + 5 = 5

     - 5  - 5

8x = 0

/8   /8

x = 0

8x – 5y = 5

8(0) - 5y = 5

0 - 5y = 5

-5y = 5

/-5   /-5

y = -1

(x,y) ==> (0,-1)

Hope this helps!

A survey of 400 randomly selected high school students determined that 925 play organized sports.
A. What is the probability that a randomly selected high school student plays organized​ sports?
B. Interpret this probability.

Answers

Answer:

It is 43%.

Step-by-step explanation:

I took the 400 and divided it by the 925. I got 0.43 and moved the decimal point over 2 spots and the answer is 43%.

Have a good day!

help me pls ヾ(•ω•`)o

Answers

Given;Area of Rectangle = 3⅓ units² = 10/3 units²Height of Rectangle = 1⅖ units = 7/5 unitsTo Find;Volume of Rectangular Prism

Now,

Volume = L × B × H

Volume = (L × B) × H

Volume = Area × H

Volume = 10/3 × 7/5 units

V = 70/15 = 14/3 or 4.7 cubic units

Thus, The answer is 14/3 or 4.7 cubic units

-TheUnknownScientist 72

Benjamin is four years younger than Kevin Williams for years less than twice Benjamin’s age and William is 22 how old are Kevin and Benjamin

Answers

this doesn't make sense. did you copy it down wrong?

Help me with this I will give brainliest

Answers

Answer:

see explanation

Step-by-step explanation:

both linear equations will have the form

y = mx + c ( m is the slope and c the y- intercept )

Chef Mate

c(n) = mn + c

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (2, 14) and (x₂, y₂ ) = (3, 18.5) ← 2 ordered pairs from the table

m = [tex]\frac{18.5-14}{3-2}[/tex] = [tex]\frac{4.5}{1}[/tex] = 4.5 , then

c(n) = 4.5n + c ( n represents ounces )

To find c substitute any ordered pair from the table into c(n)

using (4, 23 )

23 = 18 + c ⇒ c = 23 - 18 = 5

c(n) = 4.5n + 5 ← equation for Chef Mate

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

Similarly for Grocery Gourmet

g(n) = mn + c

using (2, 23 ) and (3, 27 ) to find m

m = [tex]\frac{27-23}{3-2}[/tex] = [tex]\frac{4}{1}[/tex] = 4 , then

g(n) = 4n + c

using (4, 31 ) to find c

31 = 16 + c ⇒ c = 31 - 16 = 15

g(n) = 4n + 15 ← equation for Grocery Gourmet

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

Equate the 2 equations to find when cost is the same

4.5n + 5 = 4n + 15 ( subtract 4n from both sides )

0.5n + 5 = 15 ( subtract 5 from both sides )

0.5n = 10 ( divide both sides by 0.5 )

n = 20

Then when n = 20

c(n) = 4.5(20) + 5 = 90 + 5 = 95

g(n) = 4(20) + 15 = 80 + 15 = 95

Both Chef Mate and Grocery Gourmet charge $95 for 20 ounces of extract

Is y = 3/7x -4 is it proportional or nonprotional

Answers

Answer:

Not proportional

Step-by-step explanation:

Not proportional because the line has to go through the origin

The y-intercept has to be 0, but here it is given as -4

The graph goes 4 units below the origin on the y-axis.

The correct equation would be y = 3/7x

-Chetan K

please Help Me answer this question ​

Answers

Vertex formula = -b/2a = -6/2 = -3 = x-value
Plug in x-value into equation
(-3)^2+6(-3)+8 = -1 = y-value
Vertex = (-3,-1)

Based off process of elimination the answer should be A.

i want to know what 24 multipled by 1.5 is

Answers

Answer:

36

Step-by-step explanation:

24×1.5

tips to answer quickly:

1.5 is the same as 1 + [tex]\frac{1}{2}[/tex]

(1×24)+([tex]\frac{1}{2}[/tex]×24)

24+12

36

The equation is 24x1.5 and that will equal 36 because 24x1=24 and 24x.5=12 so 12+24=36

solve for x!!!!!!!!!!

Answers

Answer:

8 10

Step-by-step explanation:

maybe this will help you

2) Find the total cost (in dollars) of buying:
a) 8 pears at 50 cents each
b) p pears at 50 cents each
c) p pears at y cents each

Answers

Answer:

a=4

b=0.5p

c=py

Step-by-step explanation:

a) 8*0.5= 4

b) p*0.5= 0.5p

c) p*y= py

Hope this helps! :)

2)Find the total cost (in dollars) of buying:
A: 4
B: 0.5
C: PY

Helpp please find the value of s! I will give brainlist

Answers

We have :

s - 39⁰+ s - 9⁰ = s + 29⁰

s + s - s = 29⁰ + 9⁰ + 39⁰

s = 77⁰

Answer: 77⁰

Ok done. Thank to me :>

Help Iḿ stuck on this problem

Answers

Here’s the work for the answer but I need twenty characters so this is a long answer lol

Answer:

774

Step-by-step explanation:

38*15=570

17*12=204

570+204=774


3) Write the following numbers from highest to lowest: 6288, -8, 2301, -282, 202

Answers

Answer:

6288 2301 202 -8 -282

im genius

plzzzzzzzzzzzzzzzzzzzzzzzzzzzzz help me

Answers

Answer:

248

Step-by-step explanation:

I'm not completely sure but hope this helps

Answer:

220 cm²

Step-by-step explanation:

area of rectangle:

Length * Width

18 * 11

198 cm²

Triangle area:

1/2 * base * height

1/2 * (18-7)(15-11)

1/2 * 11 * 4

22 cm²

So total area: 198 cm² + 22 cm² = 220 cm²

At the school store, 3 pens and 2 notebooks cost a total of $12, while 1 pen and 3 notebooks cost a total of $11. This can be represented by the system of equations, where x stands for the cost, in dollars, of pens, and y stands for the cost, in dollars, of notebooks.



What is the cost of one notebook?
A.$2.40
B.$2.75
C.$2.00
D.$3.00

Answers

Answer:

D

Step-by-step explanation:

the reason why is because if you put 3 dollars in for the notebooks right you have 3x3=9 and that one pen will be 2 dollars. Now you have 3×2=6 and then the two notebooks will be 6 and you add that and get 12. Hope this helps

Answer:

One notebook is $3.00

Step-by-step explanation:

3x + 2y = $12

1x + 3y = $11

Add -3y to the second equation

x = 11 - 3y

Substitute ( 11 - 3y ) for x in 3x + 2y = 12

3 ( 11 - 3y ) + 2y = 12

33 - 9y + 2y = 12

33 - 7y = 12

Add -33 to each side

-7y = -21

Divide each side by -7

y = 3

substitute 3 for y in x = 11 - 3y

x = 11 - 3(3)

x = 11 -9

x = 2

One notebook is $3.00

whats this v+2=v+4 please help me

Answers

Answer:

this should help

Step-by-step explanation:

U dont have to believe  me ;-;

v+2=v+4
+2−2=+4− 2
V=v+2
V-v=v+2-v
0=2
So your answer is 0=2
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