Question

Составьте систему уравнений, решите способом сложения. Задумано два числа. Если из первого числа вычесть удвоенное второе, то получится 4. Если к первому числу прибавить утроенное второе, то получится 39. Какие числа были задуманы?

Answer 1

Решение:
х-1число
у-2число
система:1 х-2у=4
             2 х+3у=39
2 уравнение домнажаем на -1
итог:система 1 х-2=4
                    2 -х-3у=-39
        складываем
-5у=-35
у=7
х-2*7=4
х-14=4
х=4+14
х=18
Ответ:(18и7)

Answer 2

X первое число
y второе число
x-2y=4
x+3y=39

умножим первое уравнение на -1
-x+2y=-4
x+3y=39

Сложим их
5y=35
y=35/5
y=7

x=4+2y
x=4+14
x=18

Answer 3

Solving a System of Equations by the Method of Addition

To solve the system of equations using the method of addition, we'll start by defining the two numbers as x and y.

Let's denote: - The first number as x - The second number as y

We are given the following information: 1. If from the first number we subtract twice the second number, the result is 4. 2. If to the first number we add three times the second number, the result is 39.

We can express this information as a system of equations:

1. Equation 1: \( x - 2y = 4 \) 2. Equation 2: \( x + 3y = 39 \)

Now, we'll solve this system of equations using the method of addition.

Solving the System of Equations

To solve the system of equations, we'll use the method of addition. This involves adding the equations together to eliminate one of the variables.

Adding Equation 1 and Equation 2: \[ (x - 2y) + (x + 3y) = 4 + 39 \] \[ 2x + y = 43 \]

Now, we have a new equation: 3. Equation 3: \( 2x + y = 43 \)

Solving for x and y

We now have a system of two equations: 1. Equation 1: \( x - 2y = 4 \) 2. Equation 3: \( 2x + y = 43 \)

We can solve this system of equations to find the values of x and y.

Multiplying Equation 1 by 2 and adding it to Equation 3: \[ 2x - 4y = 8 \] \[ 2x + y = 43 \] \[ -5y = -35 \] \[ y = 7 \]

Substituting the value of y back into Equation 1: \[ x - 2(7) = 4 \] \[ x - 14 = 4 \] \[ x = 18 \]

Conclusion

Therefore, the two numbers that were originally conceived are: - The first number, x, is 18 - The second number, y, is 7

So, the numbers that were originally conceived are 18 and 7.