Question

2x+5y=3200 3x-2y=1000

Answer 1

Ответ:

х=600, у=400

Пошаговое объяснение:

Умножить первое уравнение на 3, а второе на -2, потом сложить

6х+15у=9600

-6х+4у=-2000

19 у=7600

У=400

Теперь найдём х

2х+5*400=3200

2х=1200

х=600

Answer 2

$2x + 5y = 3200;$

$2y + 1000 = 3x$

$2x + 5y = 3200;$

$3x - 2y = 1000$

$-6x - 15y = - 9600;$

$6x - 4y = 2000$

$-19y = -7600$

$y = 400$

$2x + 2000 = 3200$

$2x = 1200$

$x = 600$

Answer 3

To solve the system of equations:

2x + 5y = 3200 ...(1) 3x - 2y = 1000 ...(2)

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

First, let's multiply equation (1) by 2 and equation (2) by 5 to eliminate the x term:

2(2x + 5y) = 2(3200) 5(3x - 2y) = 5(1000)

This simplifies the equations to:

4x + 10y = 6400 ...(3) 15x - 10y = 5000 ...(4)

Now, we can add equations (3) and (4) together to eliminate the y term:

(4x + 10y) + (15x - 10y) = 6400 + 5000

This simplifies to:

4x + 15x = 11400

Combining like terms:

19x = 11400

Dividing both sides by 19:

x = 11400 / 19 x ≈ 600

Now that we have the value of x, we can substitute it back into one of the original equations to solve for y. Let's use equation (1):

2x + 5y = 3200

Substituting x ≈ 600:

2(600) + 5y = 3200 1200 + 5y = 3200

Subtracting 1200 from both sides:

5y = 2000

Dividing both sides by 5:

y = 2000 / 5 y = 400

Therefore, the solution to the system of equations is x ≈ 600 and y = 400.