# Solve the system of equations. -4x+7y=20 y=3x+15

Solve by Substitution :

// Solve equation [2] for the variable y

[2] 5y = 15x - 4

[2] y = 3x - 4/5

// Plug this in for variable y in equation [1]

[1] 15x - 20•(3x-4/5) = 7

[1] -45x = -9

// Solve equation [1] for the variable x

[1] 45x = 9

[1] x = 1/5

// By now we know this much :

x = 1/5

y = 3x-4/5

// Use the x value to solve for y

y = 3(1/5)-4/5 = -1/5

Solution :

{x,y} = {1/5,-1/5}

## Related Questions

Simplify 2(x + 4) + 7(x – 5) + 3. Show each step of your work.

2x + 8 + 7x - 35 + 3
2x + 7x - 27 + 3
9x - 24
2(x + 4) + 7(x – 5) + 3
2x + 8 + 7x - 35 + 3 //distributive property.
9x - 23 // combine like variables

Evaluate x – 2y if x = –3 and y = –6.

For given x and y value, the value of expression is 9. Therefore, option C is the correct answer.

Given that, x - 2y if x = -3 and y = -6.

What is an expression?

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

Substitute x = -3 and y = -6 in the given expression, we get

-3 - 2(-6)

= -3+12

= 9

For given x and y value, the value of expression is 9. Therefore, option C is the correct answer.

brainly.com/question/28170201.

#SPJ2

X - 2y

x = -3 and y = -6

-3 - 2(-6)
-3 + 12
9

A team has P points. P = 3W + D

W = Wins
D = Draws

B) After 35 games a different football team has 50 points. 14 games were draw. How many games has this team lost

You would just plug it in and solve for w.

p = 3w + d
50 = 3w + 14          -subtract the 14 from both sides
36 = 3w                  - divide both sides by 3
12 = w

There were 12 wins. If they played 35 games, 12 were won and 14 were draw, you just subtract them from 35 and you get 9. The team lost 9 games.
Sub in the values and solve for W
50=3W+14
50-14=3W
36=3W
12=W
The team won 12 games.
12+14=26 (games drawn and won)
35-26=9
Therefore they lost 9 games

What points are on the graph -3x+6y+5=-7

The slope 1/2 y -intercept -2

How many different 6-digit numbers can be formed by arranging the digits in 332345?

Choose the three digits out of the 6 digits to form a three-digit number are given below.

Thus, there are 120 different ways by which a three-digit number can be formed.

What are Permutation and combination?

A permutation is an act of arranging the objects or elements in order. Combinations are the way of selecting objects or elements from a group of objects or collections, in such a way the order of the objects does not matter.

Given

The sample is (3, 3, 2, 3, 4, 5).

How many different 6-digit numbers can be formed by arranging the digits in 3,3,2,3,4,5?

Choose the three digits out of the 6 digits to form a three-digit number are given by

Thus, there are 120 different ways by which a three-digit number can be formed.

brainly.com/question/11732255

Solution-

There are digits to be arranged,they are {3,3,2,3,4,5}. And from those ,3 digits are repeated .

so the total number of distinct number that can be formed = = = 120 (ans)

Lisa purchased a hat for \$10, a purse for \$20, and a book for \$23.The sales-tax rate was 7.2 percent. What was the total amount she paid?

From information given Lisa bought three items.

10 + 20 + 23 = 53 dollars ( which is total pre- tax cost)

The sales tax rate is at 7.2% . Value of this tax in dollars will be:

7.2 % of 53 →  (7.2 / 100) × 53  →  0.072 × 53 =  3.816

So the tax rate value is 3.816

Total cost of items will be 53 + 3.816 =  56. 816

Rounded off  to the nearest cent 56.816   =  56.80

Therefore Lisa paid a total of \$ 56.80

Solve for x 2(x+9)=x+21

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

2(x+9)=x+21

(2)(x)+(2)(9)=x+21 (Distribute)

2x+18=x+21

Step 2: Subtract x from both sides.

2x+18−x=x+21−x

x+18=21

Step 3: Subtract 18 from both sides.

x+18−18=21−18

x=3

HELP!!!!!!!!!!!!!! When i go to search a question and i click on it it signs me out of brainly

Answer: sometimes it dose that if u have ether not been on brainly in a while or if u do a sertan type of question it logs u out  and then you will have to re log in and if it dose that all the time u click on a question you might need to report a bug to brainly hope i helped :)

A die is rolled. If you roll a 1, 2 or 3, you will toss 10 coins. If you roll a 4, 5 or 6, you will toss 20 coins. Let X denote the number of heads tossed. a) Determine the support of X. b) Determine the mean of X. c) Determine the variance of X.

a) The support of X is {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20}

b) The mean of X is 7.5

c) The variance of X is 10

Step-by-step explanation:

a) Since you can toss up to 20 coins, and from that you can obtain any number of heads from 0 to 20, then the support of X {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20}.

b) To compute the mean of X, we need to see how is the behavior of X. Since 3 dices will gives 10 coins to toss and the other 3 will give us 20, then there is a probability of 1/2 that we tossed 10 coins and a probability of 1/2 that we tossed 20.

The random variable X, conditioned to the event 'The dice is 1,2 or 3' (or equivalently, 10 coins are tossed), will have a binomial distribution with paramenters n = 10, p = 1/2. The mean of X in this case is np = 5. If X is conditioned to the event 'The dice is 4,5 or 6', then X will have also binomial distribution, but this time with paramenters n = 20, p = 1/2. The mean of X in this case is 20*1/2 = 10.

Since each event we conditioned in had probability 1/2 to occur, then E(X) = 1/2 * 5 + 1/2 * 10 = 7.5.

c) Remember that V(X) = E(X²)- E(X)². Since we alredy know the mean of X, we just need to compute the mean of X squared.

The variance of a binomial distribution Z with paramenters n and p is

V(Z) = np(1-p)

since V(Z) = E(Z²)- E(Z)² = E(Z²)- n²p², then

E(Z²) = V(Z) + E(Z)² = np(1-p) + n²p² = p²(n²-n) + np

Therefore

E(X²) = E(X² | 10 coins are tossed) * 1/2 + E(X² | 20 coins are tossed) * 1/2 =

1/2*(0.5²(10²-10) + 5) + 1/2*(0.5²(20²-20) + 10) = 13.75 + 52.5 = 66.25

As a consecuence

V(X) = 66.25 - 7.5² = 10

The variance of X is 10.

a) The support of X is {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20}

b) The mean of X is 7.5

c) The variance of X is 10

Step-by-step explanation:

a) Since you can toss up to 20 coins, and from that you can obtain any number of heads from 0 to 20, then the support of X {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20}.

b) To compute the mean of X, we need to see how is the behavior of X. Since 3 dices will gives 10 coins to toss and the other 3 will give us 20, then there is a probability of 1/2 that we tossed 10 coins and a probability of 1/2 that we tossed 20.

The random variable X, conditioned to the event 'The dice is 1,2 or 3' (or equivalently, 10 coins are tossed), will have a binomial distribution with paramenters n = 10, p = 1/2. The mean of X in this case is np = 5. If X is conditioned to the event 'The dice is 4,5 or 6', then X will have also binomial distribution, but this time with paramenters n = 20, p = 1/2. The mean of X in this case is 20*1/2 = 10.

Since each event we conditioned in had probability 1/2 to occur, then E(X) = 1/2 * 5 + 1/2 * 10 = 7.5.

c) Remember that V(X) = E(X²)- E(X)². Since we alredy know the mean of X, we just need to compute the mean of X squared.

The variance of a binomial distribution Z with paramenters n and p is

V(Z) = np(1-p)

since V(Z) = E(Z²)- E(Z)² = E(Z²)- n²p², then

E(Z²) = V(Z) + E(Z)² = np(1-p) + n²p² = p²(n²-n) + np

Therefore

E(X²) = E(X² | 10 coins are tossed) * 1/2 + E(X² | 20 coins are tossed) * 1/2 =

1/2*(0.5²(10²-10) + 5) + 1/2*(0.5²(20²-20) + 10) = 13.75 + 52.5 = 66.25

As a consecuence

V(X) = 66.25 - 7.5² = 10

The variance of X is 10.by-step explanation: