Question

3х-у=4 2х+3у=10 решите систему плиз

Answer 1

Используем метод вычитания второго уравнения из первого:

   3х-у=4

-

   2х+3у=10

т.е 3х-2х; -у-3у; 4-10

выходит:

x-4y=-6

выражаем х:

х=4у-6

подставляем в любое из уравнений:

3(4у-6)-у=4

12у-18-у=4

11у=22

у=2

тогда х = 4*2-6=8-6=2

Ответ: x=2; y=2

Answer 2

To solve the system of equations, we can use either the substitution method or the elimination method. I'll demonstrate the elimination method here.

Given the system of equations:

1. 3x - y = 4
2. 2x + 3y = 10

Step 1: Multiply the first equation by 3 to make the coefficients of y in both equations the same.

1. 3(3x - y) = 3(4) 9x - 3y = 12

Step 2: Now, we'll add the modified first equation (9x - 3y = 12) to the second equation (2x + 3y = 10) to eliminate the y variable.

(9x - 3y) + (2x + 3y) = 12 + 10 11x = 22

Step 3: Divide both sides by 11 to solve for x:

x = 22 / 11 x = 2

Step 4: Substitute the value of x back into one of the original equations to solve for y. Let's use the first equation:

3x - y = 4 3(2) - y = 4 6 - y = 4

Step 5: Now, solve for y:

-y = 4 - 6 -y = -2

Divide both sides by -1 to get the positive value of y:

y = 2

Step 6: Verify the solution by substituting the values of x and y into the second equation:

2x + 3y = 10 2(2) + 3(2) = 10 4 + 6 = 10 10 = 10

Both equations are satisfied when x = 2 and y = 2. Therefore, the solution to the system of equations is x = 2 and y = 2.