Question

2 (х+3у)+9=х+6 и 3 (х-2у)=х+30 это система решите способом сложения

Answer 1

Раскрываем скобки. 2х + 6у + 9 = х + 6, 3х - 6у = х + 30; 2х - х + 6у = 6 - 9, 3х - х - 6у = 30; х + 6у = - 3, 2х - 6у = 30; Сложим уравнения данной системы, для этого слаживаем коэффициенты с переменной "х", потом слаживаем коэффициенты с переменной "у", а потом свободные члены(после знака равно). (х + 2х) + (6у - 6у) = -3 + 30; 3х = 27; х = 27 : 3; х = 9; Подставим значение переменной "х" в первое уравнение: 9 + 6у = - 3; 6у = - 3 - 9; 6у = - 12; у = - 12 : 6; у = - 2. Ответ: (9; - 2).

Answer 2

To solve the system of equations using the method of addition (also known as the method of elimination or the method of balancing), we'll add the two equations together in such a way that one of the variables gets eliminated, leaving us with a single equation that we can solve for the remaining variable.

The given system of equations is:

1. 2(x + 3y) + 9 = x + 6
2. 3(x - 2y) = x + 30

Step 1: Simplify the equations: For equation 1, distribute the 2 on the left side: 2x + 6y + 9 = x + 6

For equation 2, distribute the 3 on the left side: 3x - 6y = x + 30

Step 2: Rearrange both equations so that the variables are on one side and constants on the other side:

Equation 1: 2x + 6y - x = 6 - 9 x + 6y = -3

Equation 2: 3x - x - 6y = 30 2x - 6y = 30

Step 3: Now, we need to eliminate one of the variables by adding the two equations:

(x + 6y) + (2x - 6y) = -3 + 30

Combine like terms: 3x = 27

Step 4: Solve for x: x = 27 / 3 x = 9

Step 5: Substitute the value of x (which is 9) into one of the original equations to find y. Let's use Equation 1:

x + 6y = -3 9 + 6y = -3

Step 6: Solve for y: 6y = -3 - 9 6y = -12

y = -12 / 6 y = -2

So, the solution to the system of equations is x = 9 and y = -2.