Question

2x+3y=10 x-2y=-5 решите систему

Answer 1

Решение задания приложено

Answer 2

Умножаем на 2. Вычитаем. Получается 10у=30

У=3

Подставим

2х+9=10

2х=1

Х=1.

Ответ:х=1; у=3;

Answer 3

To solve the system of equations:

1. 2x + 3y = 10
2. x - 2y = -5

There are multiple methods to solve a system of equations, such as substitution, elimination, or using matrices. I'll use the elimination method to solve this system:

Step 1: Multiply both sides of equation (2) by 3 to make the coefficients of y in both equations equal:

2x + 3y = 10 (equation 1) 3(x - 2y) = 3(-5) (equation 2 multiplied by 3)

Step 2: Simplify equation (2):

2x + 3y = 10 3x - 6y = -15

Step 3: Add the two equations to eliminate y:

(2x + 3y) + (3x - 6y) = 10 - 15

Step 4: Simplify the equation:

5x - 3y = -5

Step 5: Now, we have two equations:

2x + 3y = 10 5x - 3y = -5

Step 6: Add the two equations to eliminate y:

(2x + 3y) + (5x - 3y) = 10 - 5

Step 7: Simplify the equation:

7x = 5

Step 8: Isolate x by dividing both sides by 7:

x = 5 / 7

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

2x + 3y = 10

Substitute x = 5 / 7:

2 * (5 / 7) + 3y = 10

Step 10: Solve for y:

10/7 + 3y = 10

Subtract 10/7 from both sides:

3y = 10 - 10/7

Step 11: Simplify:

3y = (70 - 10) / 7

3y = 60 / 7

Step 12: Divide by 3 to isolate y:

y = 60 / 7 * 1/3

Step 13: Simplify:

y = 20 / 7

So, the solution to the system of equations is:

x = 5 / 7 y = 20 / 7