Solve the following pair of linear equations using substitution method


[tex] x-3y = 13[/tex]

[tex]x+2y=8[/tex]

Answers

Answer 1

Answer:

(10, - 1 )

Step-by-step explanation:

Given the 2 equations

x - 3y = 13 → (1)

x + 2y = 8 → (2)

Rearrange (1) making x the subject by adding 3y to both sides

x = 3y + 13 → (3)

Substitute x = 3y + 13 into (2)

3y + 13 + 2y = 8

5y + 13 = 8 ( subtract 13 from both sides )

5y = - 5 ( divide both sides by 5 )

y = - 1

Substitute y = - 1 into (3) for corresponding value of x

x = 3(- 1) + 13 = - 3 + 13 = 10

solution is (10, - 1 )


Related Questions

Find an equation for the line below.

Answers

Answer:

y= -1/4x+ 3.75

Step-by-step explanation:

help me please I have no clue how to do these

Answers

Answer:

AB is parallel to DC

Step-by-step explanation:

you have to tilt your head to the left for this one LOL

AB is parallel to DC

since 1 = 6

its the bottom of a triangle

People at the state fair were surveyed about which type of lemonade they preferred. The results are shown below. Pink lemonade: 156 males, 72 females Yellow lemonade: 104 males, 48 females The events "prefers pink lemonade" and "female" are independent because P(pink lemonade | female) = P(pink lemonade) = 0.6. P(female | pink lemonade ) = P(pink lemonade) = 0.3. P(pink lemonade | female) = 0.3 and P(pink lemonade) = 0.6. P(female | pink lemonade ) = 0.3 and P(pink lemonade) = 0.6.

Answers

Answer:

[tex]P(pink) = P(pink |\ female) = 0.6[/tex]

Step-by-step explanation:

Given

[tex]\begin{array}{ccc}{} & {Male} & {Female} & {Pink} & {156} & {72} \ \\ {Yellow} & {104} & {48} \ \end{array}[/tex]

Required

Why [tex]prefers\ pink\ lemonade[/tex] and [tex]female[/tex] are independent

First, calculate [tex]P(pink |\ female)[/tex]

This is calculated as:

[tex]P(pink |\ female) = \frac{n(pink\ \&\ female)}{n(female)}[/tex]

[tex]P(pink |\ female) = \frac{72}{48+72}[/tex]

[tex]P(pink |\ female) = \frac{72}{120}[/tex]

[tex]P(pink |\ female) = 0.6[/tex]

Next, calculate [tex]P(pink)[/tex]

[tex]P(pink) = \frac{n(pink)}{n(Total)}[/tex]

[tex]P(pink) = \frac{156 + 72}{156 + 72 + 104 + 48}[/tex]

[tex]P(pink) = \frac{228}{380}[/tex]

[tex]P(pink) = 0.6[/tex]

So, we have:

[tex]P(pink) = P(pink |\ female) = 0.6[/tex]

Hence, they are independent

Answer:

P(pink lemonade | female) = P(pink lemonade) = 0.6.

Step-by-step explanation:

A

If P(A) = 2/3, P(B) = 4/5 and P(AnB) = 3/5, what is P(AuB)?

Answers

Answer:

13/15

Step-by-step explanation:

P(A∪B) = P(A) + P(B) – P(A∩B)

            = 2/3 + 4/5 - 3/5

 Getting a common denominator

            2/3 *5/5 + 4/5*3/3  - 3/5 *3/3

             10/15 + 12/15 - 9/15

             13/15

Answer:

[tex] \frac{13}{15} [/tex]

Step-by-step explanation:

We know that,

P(AUB) = P(A) + P(B) - P(A n B)

So,

[tex]P(AUB) = P(A) + P(B) - P(A n B) \\ = \frac{2}{3} + \frac{4}{5} - \frac{3}{5} \\ = \frac{10 + 12 - 9}{15} \\ = \frac{22 - 9}{15} \\ = \frac{13}{15} [/tex]

hope this helps you.

Have a nice day!

# By selling 5 oranges, a shopkeeper gains the selling price of 1 orange. Find his profit percentage.
O 50%
O 25%
O 15%
O 20%​

Answers

profit from selling 5 oranges is 20%

Profit percentage of  selling 5 oranges, a shopkeeper gains the selling price of 1 orange is equals to 25%.

What is profit?

" Profit is defined as difference of cost price from selling price when the selling price of a product is greater than its cost price."

Formula used

Profit percentage = [tex]\frac{Selling price - cost price}{cost price} (100)[/tex]

According to the question,

We know that,

Selling price = cost price + profit

Substitute the given condition in the selling price formula we get,

Selling price of 5 oranges

= Cost price of 5 oranges + Selling price of 1 oranges

⇒(S.P of 5 oranges) - (S.P of 1 oranges) = C.P. of 5 oranges

S.P of 4 oranges = C.P of 5 oranges

⇒[tex]\frac{S.P}{C.P}=\frac{5}{4}[/tex]

Substitute the value in the formula to get profit percentage,

Profit percentage = [tex]\frac{5-4}{4}(100)[/tex]

                              = 25%

Hence, profit percentage of  selling 5 oranges, a shopkeeper gains the selling price of 1 orange is equals to 25%.

Learn more about profit here

https://brainly.com/question/15036999

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Which linear inequality represents the graph below? (-2, 3) & (0, -2)​

Answers

Answer:

no hablo inglés wey perdón corona y gracias

someone help me please with this algebra problem

Answers

Answer:

L=65-15d; continuous

Step-by-step explanation: L stands for the length of the leaf, 65 stands for the original length of the leaf(which will decrease), d stands for the days. the answer is L=65-15d continuous because the original size of the leaf when he bought it was 65(which can decrease over time), every afternoon he cuts the leaf by 15 (which means the size of the leaf is decreasing and by 15 every day) which gives me -15d, if he cuts the leaf by 15 every day and never changes the length of the cut then the function is continuous

P÷✓2=✓t/r+q

express t in the terms of p and q​

Answers

Given:

Consider the given equation is:

[tex]p\div \sqrt{2}=\sqrt{\dfrac{t}{r+q}}[/tex]

To find:

The value of t in terms of p, q and r.

Solution:

We have,

[tex]p\div \sqrt{2}=\sqrt{\dfrac{t}{r+q}}[/tex]

It can be written as:

[tex]\dfrac{p}{\sqrt{2}}=\sqrt{\dfrac{t}{r+q}}[/tex]

Taking square on both sides, we get

[tex]\dfrac{p^2}{2}=\dfrac{t}{r+q}[/tex]

Multiply both sides by (r+q).

[tex]\dfrac{p^2(r+q)}{2}=t[/tex]

Therefore, the required solution is [tex]t=\dfrac{p^2(r+q)}{2}[/tex].

Help me solve this problem please

Answers

Answer:

c

Step-by-step explanation:

You usually buy a 16.5 16.5 -ounce bottle of shampoo. There is a new bottle that says it gives you 30% 30 % more free. Use the drop-down menus to build an equation that could be used to find the size of the larger bottle,

Answers

Answer:

21.45 oz

Step-by-step explanation:

(16.5*0.3)+16.5=x

(4.95)+16.5=x

21.45

Answer:

top x-16.5

bottom 16.5

Step-by-step explanation:

im right

Help mee A scout troop are hiking in a forest. Starting from their base, they walk 4.2km south followed by 7.1km west. They want to walk the shortest distance back to their base. On what bearing should the scouts walk?

Answers

Answer:

They should walk on a bearing of 59.4 degrees

Step-by-step explanation:

Given

[tex]South = 4.2km[/tex]

[tex]West = 7.1km[/tex]

Required

The bearing back to the base

The given question is illustrated with the attached image.

To do this, we simply calculate the measure of angle a using:

[tex]\tan(a) = \frac{Opposite}{Adjacent}[/tex]

[tex]\tan(a) = \frac{7.1}{4,2}[/tex]

[tex]\tan(a) = 1.6905[/tex]

Take arctan of both sides

[tex]a = \tan^{-1}(1.6905)[/tex]

[tex]a = 59.4^o[/tex]

The bearing that the scout should work is N59.4W for the shortest distance

Trigonometric ratio

Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.

Let  A represent the angle that the scouts walk

tan∠A = 4.2/7.1

A = 30.6°

The bearing that the scout should work is N59.4W (90 - 30.6) for the shortest distance

Find out more on Trigonometric ratio at: https://brainly.com/question/4326804

In ΔTUV, the measure of ∠V=90°, UT = 65, VU = 56, and TV = 33. What ratio represents the cosine of ∠T?

Answers

Answer: The ratio that represents the cosine of ∠T is [tex]\frac{56}{65}[/tex]

Step-by-step explanation:

We are given:

UV = 56 units

VT = 33 units

UT = 65 units

∠V = 90°

Cosine of an angle is equal to the ratio of base and the hypotenuse of the triangle. ΔTUV is drawn in the image below.

[tex]\cos \theta=\frac{\text{base}}{\text{hypotenuse}}[/tex]

Base of the triangle is UV and the hypotenuse of the triangle is TU

Putting values in above equation, we get:

[tex]\cos \theta=\frac{UV}{TU}=\frac{56}{65}[/tex]

Hence, the ratio that represents the cosine of ∠T is [tex]\frac{56}{65}[/tex]

WILL MARK BRAINLIEST

Please help solve problems with common tangents.

Thank you.

Answers

Answer:

sorry I don't know but can u PLEASE MARK ME AS BRAINLIEST.

Step-by-step explanation:

.......

Answer:  12

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

Explanation:

Let's start with what the hint gives us. So the first sub-goal is to prove triangle ABE is similar to triangle DCE.

Since points A and D are points of tangency, this means the radii of each of those circles is perpendicular to the common internal tangent. So angles EAB and EDC are 90 degrees each.

Due to the vertical angle theorem, we also know that angles AEB and DEC are the same (we don't know the measure but we know they're equal angles).

So we have two pairs of congruent corresponding angles between the triangles, which is sufficient to let us use the AA (angle angle) similarity theorem. Therefore, the triangles have been proven to be similar. Triangle DCE is a reduced scaled down copy of triangle ABE. Or in reverse, triangle ABE is an enlarged copy of triangle DCE.

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

Since the triangles are similar, we can form the proportion below and solve for x

AB/AE = DC/DE

x/18 = 4/6

x*6 = 18*4 .... cross multiplication

6x = 72

x = 72/6

x = 12

Therefore, segment AB is 12 units long, and this is the radius of circle B.

Which of the following values of r will result in a true statement when substituted into the given equation?

2(4r + 4) = -16

A. r = -3
B. r = -2
C. r = 2
D. r = 3

Answers

I think that it is A I guessed

sharon is planning a holiday for 4 people for 7 days

Answers

just multiply the numbers together, and it gives you 28, which is what she did thought everything

please help urgent !!!

Answers

Answer:

The answer is "sugar= 200g, flour=600g, and butter=400g".

Step-by-step explanation:

[tex]50\ g \ sugar = 15\ biscuits\\\\3 \times 50 \ g = flour \\\\150\ g = flour\\\\2 \times 50 \ g = butter \\\\ 100 \ g = butter\\\\\frac{60}{15} = 4\\\\ 4 \ \text{times as much}\\\\4 \times 50\ g = 200\ g \ of\ sugar\\\\4 \times 150\ g = 600\ g \ of\ flour\\\\4 \times 100\ g = 400\ g \ of\ butter\\\\[/tex]

in a two digit number the tens digit is 6 more than the units digit. if the digits are interchanged, the sum of the new and the original number is 132. Determine the original number.​

Answers

Given:

In a two digit number the tens digit is 6 more than the units digit.

If the digits are interchanged, the sum of the new and the original number is 132.

To find:

The original number.

Solution:

Let the unit digit of the original number be x. So, the tens digit is (x+6) and the value of the number is:

[tex]m=(x+6)\times 10+x\times 1[/tex]

[tex]m=10x+60+x[/tex]

[tex]m=11x+60[/tex]

If we interchange the digits, then the value of new number is:

[tex]n=x\times 10+(x+6)\times 1[/tex]

[tex]n=10x+x+6[/tex]

[tex]n=11x+6[/tex]

The sum of the new and the original number is 132.

[tex]m+n=132[/tex]

[tex]11x+60+11x+6=132[/tex]

[tex]22x+66=132[/tex]

[tex]22x=132-66[/tex]

[tex]22x=66[/tex]

Divide both sides by 22.

[tex]x=\dfrac{66}{22}[/tex]

[tex]x=3[/tex]

So, the unit digit of the original number is 3 and the tens digit is:

[tex]x+6=3+6[/tex]

[tex]x+6=9[/tex]

Therefore, the original number is 39.

question is in the pucture

Answers

Answer:

Aiden earned less money for his 8th than he earned for his 4th drive.

[tex]ANSWER:C[/tex]

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

HOPE IT HELPS

HAVE A GREAT DAY!!

Please help


[tex]a { }^{2} + b {}^{2} + 18 \geqslant 6(a - b)[/tex]

Answers

Answer:

a²+b²-18greaterthan or equal to 6a-6b

Which function has a vertex at (2, 6)?
O f(x) = 2|x – 2| – 6
O f(x) = 2|x – 2| + 6
Of(x) = 2|x + 2| + 6
Of(x) = 2|x + 2| - 6

Answers

Answer:

B

Step-by-step explanation:

Trust me bro. It’s “B.”

Please help me with this

Answers

Answer:

The surface area of the pyramid is 16.65 m^2.

Step-by-step explanation:

Jose and a group of friends bought concert tickets for $257. The booking agency also charged a fee, bringing the total cost to $274.99. The amount of change is $17.99.
What is the percent increase in the cost due to the fee?

Answers

Answer: hello there here is your answer:

7%

Step-by-step explanation:

if you divide the difference between the two numbers it will give you a decimal ....you need to convert that decimal into a percent which is 7%

hope this help have a good day bye

Answer:

the other person is correct

Step-by-step explanation:

graphical representation of the function x = f( y) shows that the zeroes will come on​

Answers

Answers

The zeros of a function represent the x-intercept(s) when the function is graphed. The zeros of a function represent the root(s) of a function.

I need help pleaseeee

Answers

Answer is:
9.8df+5.8dg+13.1fg
Assuming you add both numbers together for each side of the triangle.

which of the points lies on the curve y=x^3

Answers

Answer:

D

Step-by-step explanation:

Hello,

A: no since (1/3)^3=1/27 not 1/9

B: no since (-1)^3=-1 not 1

C: no since (-2)^3=-8 not -6

D: yes since (-1/2)^3=-1/8

Answser D

A solid wooden block in the shape of a rectangular prism has a length, width and height

Answers

Step-by-step explanation:

Volume of the block

[tex] = lbh[/tex]

[tex] = \frac{3}{8} \times \frac{1}{8} \times \frac{5}{8} [/tex]

[tex] = \frac{3 \times 5}{ {8}^{3} } [/tex]

[tex] = \frac{15}{512} [/tex]

solve the equation x^2 -100 = 0

Answers

The answer would be 10



:)

The area (A) of a circle is a function of its radius (r) and is given by the function A=f(r)=pie r^2. What is the domain of this function
A. All positive real numbers
B. All real numbers
C. All positive real numbers including 0
D. All real numbers excluding fraction

Answers

all positive real numbers. in this function, the domain is the radius. all real numbers includes negative numbers, and u cant have a negative distance. you also cant have a radius of 0 because the circle wouldnt exist. and u can have a fraction domain, so A is the answer

what is a square plus b square?????????????????

Answers

Answer:

c squared

Step-by-step explanation:

Answer:

C Squared

Step-by-step explanation:

BRAINLIEST FOR CORRECT ANSWER

Answers

Answer:

y=-2x+6

Step-by-step explanation:

For this question, you need the slope-intercept form which is y=mx+b, where m is the slope and b is the y-intercept. We should first find the slope of the equation. The slope is the rise-over-run; this means that the slope is equal to the difference in y over x. One way to find the slope is to count the difference between the two coordinates or you can use the formula. Either way, the y decreases by 2, and the x increases by 1. Therefore, the slope is -2.

Then, find the intercept. One way to do this by plugging in one of the coordinates into the equation we have so far, y=-2x+b. So, plug 4 in for y and 1 in for x; 4=-2(1)+b. Next, solve for b. This equals b=6.

Finally, plug in the slope and intercept for the final answer, y=-2+6.

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