Question

решите систему способом сложения: 2х+y=6 -4х+3у=8. решите задачу с помощью системы уравнений. за покупку канцтоваров на сумму 65к.таня расплатилась пяти-и десятикопеечными монетами.всего она отдала 9 монет. сколько среди них было пятикопеечных и сколько десятикопеечных? ЛЮДИ ПОМОГИТЕ ПОЖАЙЛУСТА МНЕ НАДО ПРОРЕШАТЬ А Я ЭТУ ТЕМУ НЕЗНАЮ!!!ПОЖЕ УМОЛЯЮЮЮЮ

Answer 1

2x+y=6   )  *2         4x+2y=12         5y=20     2x+4=6  

-4x+3y=8  )               -4x+3y=8            y=4      x=1

Ответ : (1;4)

Пусть х-количество 5-ти копеечных монет , а у- количество 10ти копеечных монет .

Тогда(  х+у ) - количество монет , или 9 , а (5х+10у )- сумма , или 65 . составим и решим систему .

х+у=9              x=9-y

5x+10y=65    5x+10y=65

    

5(9-y) +10y =65

45 - 5y+10y=65

5y=20

y=4                  x+4=9

                             x=5

Ответ : 5 пятикопеечных , 4 десятикопеечных

 

Answer 2

решила пока только систему уравнений

 

Answer 3

Solving the System of Equations

To solve the system of equations using the method of addition, we will eliminate one variable by adding the two equations together. Let's solve the system step by step:

Given system of equations: 1. 2x + y = 6 2. -4x + 3y = 8

To eliminate the variable "x," we will multiply equation 1 by 2 and equation 2 by 1, and then add the resulting equations together:

3. (2 * (2x + y)) + (1 * (-4x + 3y)) = (2 * 6) + (1 * 8) Simplifying equation 3: 4x + 2y - 4x + 3y = 12 + 8 5y = 20 y = 4

Now that we have the value of "y," we can substitute it back into one of the original equations to solve for "x." Let's substitute it into equation 1:

4. 2x + 4 = 6 Subtracting 4 from both sides: 2x = 2 x = 1

Therefore, the solution to the system of equations is x = 1 and y = 4.

Solving the Coin Problem

To solve the coin problem, let's assign variables to the number of five-kopeck coins and ten-kopeck coins that Tanya used. Let's say the number of five-kopeck coins is "x" and the number of ten-kopeck coins is "y."

According to the problem, Tanya used a total of 9 coins and the total value of the coins is 65 kopecks. We can set up the following system of equations:

1. x + y = 9 (equation representing the total number of coins) 2. 5x + 10y = 65 (equation representing the total value of the coins)

To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of substitution:

From equation 1, we can express x in terms of y: x = 9 - y

Substituting this value of x into equation 2: 5(9 - y) + 10y = 65 45 - 5y + 10y = 65 5y = 20 y = 4

Now that we have the value of y, we can substitute it back into equation 1 to solve for x: x + 4 = 9 x = 5

Therefore, Tanya had 5 five-kopeck coins and 4 ten-kopeck coins.

I hope this helps! Let me know if you have any further questions.