Question

Найдите решение системы уравнений способом сложения: { 7x2y=9 {5x+2y=11 { - это большая фигурная скобка. {9x-2y=11 {x-2y=7 Смотреть ответ Valeriya05 Valeriya05 Если в первой системе уравнений в первом уравнении между двумя переменными знак "+", то решение верное.

Answer 1

Solution to the System of Equations by Addition Method:

To solve the system of equations using the addition method, we need to eliminate one variable by adding or subtracting the equations. Let's solve the given system of equations step by step:

Equation 1: 7x + 2y = 9 (Equation A) Equation 2: 5x + 2y = 11 (Equation B) Equation 3: 9x - 2y = 11 (Equation C) Equation 4: x - 2y = 7 (Equation D)

To eliminate the variable "y," we can add Equation A and Equation B:

(Equation A) + (Equation B): (7x + 2y) + (5x + 2y) = 9 + 11 12x + 4y = 20

Now, let's eliminate the variable "y" by adding Equation C and Equation D:

(Equation C) + (Equation D): (9x - 2y) + (x - 2y) = 11 + 7 10x - 4y = 18

We now have two equations: 12x + 4y = 20 (Equation E) 10x - 4y = 18 (Equation F)

To eliminate the variable "y," we can add Equation E and Equation F:

(Equation E) + (Equation F): (12x + 4y) + (10x - 4y) = 20 + 18 22x = 38

Dividing both sides of the equation by 22, we get: x = 38/22 x = 1.7273 (rounded to four decimal places)

Now, substitute the value of x back into one of the original equations to solve for y. Let's use Equation D:

x - 2y = 7 1.7273 - 2y = 7 -2y = 7 - 1.7273 -2y = 5.2727 y = 5.2727 / -2 y = -2.6364 (rounded to four decimal places)

Therefore, the solution to the given system of equations is: x ≈ 1.7273 y ≈ -2.6364

Please note that the solution is approximate due to rounding.

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