Question

Номер 1 найдите решение системы уравнений способом подстановки 1)3 (x+2y) - y= 27 4 (x + y) - 3x =23 2)2x + 3 (x + y)=11 7(x+ 3y) - 6x=-59 Номер 2 составьте систему уравнений и решите ее способом подстановки Сумма двух чисел равна 58 Первое число на 8 больше второго Найдите эти числа Первое число x На 8 больше чем второе Второе число y Всего 58 ПЛИЗ ПО БЫСТРОМУ ОТО НЕ УСПЕЮ МОЖЕТЕ НЕ ДЕЛАТЬ НОМЕР 1 уравнение номер 1 я сделал мне нужно второе уравнение и номер 2

Answer 1

2х+3х+3у=11
5х+3у=11 это первое уравнение системы
7х+21у-6х=-59
х=-21у-59 это второе, подставим его в первое уравнение вместо х.
5(-21у-59)+3у=11
-105 у - 295 +3у=11
-102 у = 295+11
-102 у=306
у=-3
х=-21*(-3)-59=63-59=4
ответ х=4, у=-3

2) х+у=58
х-у=8 
х=58-у
58-у-у=8
-2у=-50
у=25
х=58-25=33

Answer 2

Solution to System of Equations using Substitution Method

Let's solve the given system of equations using the substitution method.

Equation 1: 3(x + 2y) - y = 27 ----(1)

Equation 2: 4(x + y) - 3x = 23 ----(2)

To solve this system of equations, we'll start by solving Equation 1 for x in terms of y.

From Equation 1: 3(x + 2y) - y = 27

Expanding and simplifying: 3x + 6y - y = 27 3x + 5y = 27 ----(3)

Now, we'll solve Equation 3 for x: 3x = 27 - 5y x = (27 - 5y)/3 ----(4)

Now, we'll substitute the value of x from Equation 4 into Equation 2 and solve for y.

From Equation 2: 4(x + y) - 3x = 23

Substituting the value of x from Equation 4: 4((27 - 5y)/3 + y) - 3((27 - 5y)/3) = 23

Simplifying the equation: 4(27 - 5y + 3y)/3 - (27 - 5y) = 23 (108 - 20y + 12y)/3 - 27 + 5y = 23 (108 - 8y)/3 - 27 + 5y = 23 (108 - 8y - 81 + 15y)/3 = 23 (27 + 7y)/3 = 23 27 + 7y = 69 7y = 69 - 27 7y = 42 y = 42/7 y = 6

Now that we have the value of y, we can substitute it back into Equation 4 to find the value of x.

From Equation 4: x = (27 - 5y)/3

Substituting the value of y = 6: x = (27 - 5(6))/3 x = (27 - 30)/3 x = -3/3 x = -1

Therefore, the solution to the system of equations is: x = -1 y = 6

System of Equations for Finding Two Numbers

Let's now solve the second problem of finding two numbers using the substitution method.

We are given the following information: - The sum of two numbers is 58. - The first number is 8 more than the second number.

Let's assume the first number as x and the second number as y.

From the given information, we can form the following system of equations:

Equation 1: x + y = 58 ----(5)

Equation 2: x = y + 8 ----(6)

To solve this system of equations, we'll substitute the value of x from Equation 2 into Equation 1 and solve for y.

Substituting the value of x from Equation 2 into Equation 1: (y + 8) + y = 58

Simplifying the equation: 2y + 8 = 58 2y = 58 - 8 2y = 50 y = 50/2 y = 25

Now that we have the value of y, we can substitute it back into Equation 2 to find the value of x.

From Equation 2: x = y + 8

Substituting the value of y = 25: x = 25 + 8 x = 33

Therefore, the two numbers are: x = 33 y = 25

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