Question

Решите систему уравнений 1) 2x+ y = 5 3x - 4 y = 24 X - 2y = 9 2) 2x+ 3y = -1 3x + 5y = 1 5x + 9y = 5 До утра! Даю 65 баллов!

Answer 1

Ответ:

1) Щоб розв'язати цю систему, ми можемо використати метод елімінації:

Множимо перше рівняння на 2, а друге на 3, і додаємо їх:

4x + 2y = 10

9x - 12y = 72

Знову множимо перше рівняння на 1 і додаємо до третього рівняння:

x - 2y = 9

4x      = 19

x = 19/4

Підставляємо x у перше рівняння і знаходимо y:

2(19/4) + y = 5

y = -3/4

Таким чином, розв'язок системи рівнянь буде x = 19/4, y = -3/4.

2) Множимо перше рівняння на 3 і віднімаємо від другого:

2x + 3y = -1

-4x - 4y = 4

Тепер множимо перше рівняння на 5 і віднімаємо від третього:

10x + 15y = -5

-4x - 4y = 4

Отримали систему:

-4x - 4y = 4

10x + 15y = -5

Множимо перше рівняння на -5/4:

x + y = -1

Підставляємо x + y в друге рівняння:

10x + 15y = -5

10(x + y) = -5

x + y = -1/2

Отже, ми отримали систему:

x + y = -1/2

x + y = -1

Ця система не має розв'язку, оскільки дві лінії паралельні і не перетинаються.

Объяснение:

Answer 2

Ответ:

Ответ на фото:⬆️⬆️⬆️⬆️⬆️⬆️⬆️⬆️

Answer 3

Solution to the System of Equations:

To solve the given system of equations:

1) 2x + y = 5 3x - 4y = 24 x - 2y = 9

2) 2x + 3y = -1 3x + 5y = 1 5x + 9y = 5

Let's solve each system separately.

System 1:

To solve the first system of equations, we can use the method of substitution or elimination. Let's use the method of elimination:

Multiply the first equation by 2: 2(2x + y) = 2(5) 4x + 2y = 10

Now, subtract the second equation from the first equation: (4x + 2y) - (3x - 4y) = 10 - 24 4x + 2y - 3x + 4y = -14 x + 6y = -14 ----(1)

Multiply the third equation by 2: 2(x - 2y) = 2(9) 2x - 4y = 18

Now, add the third equation to the first equation: (x + 6y) + (2x - 4y) = -14 + 18 3x + 2y = 4 ----(2)

We now have a system of two equations: x + 6y = -14 ----(1) 3x + 2y = 4 ----(2)

To solve this system, we can multiply equation (1) by 3 and equation (2) by 2 to eliminate y:

3(x + 6y) = 3(-14) 9x + 18y = -42

2(3x + 2y) = 2(4) 6x + 4y = 8

Now, subtract the second equation from the first equation: (9x + 18y) - (6x + 4y) = -42 - 8 9x + 18y - 6x - 4y = -50 3x + 14y = -50 ----(3)

Now, we have a system of two equations: 3x + 14y = -50 ----(3) 3x + 2y = 4 ----(2)

Subtract equation (2) from equation (3): (3x + 14y) - (3x + 2y) = -50 - 4 3x + 14y - 3x - 2y = -54 12y = -54 y = -54/12 y = -4.5

Substitute the value of y into equation (2) to find x: 3x + 2(-4.5) = 4 3x - 9 = 4 3x = 4 + 9 3x = 13 x = 13/3 x = 4.33

Therefore, the solution to the first system of equations is: x = 4.33 y = -4.5

System 2:

To solve the second system of equations, we can also use the method of elimination:

Multiply the first equation by 2: 2(2x + 3y) = 2(-1) 4x + 6y = -2

Now, subtract the second equation from the first equation: (4x + 6y) - (3x + 5y) = -2 - 1 4x + 6y - 3x - 5y = -3 x + y = -3 ----(4)

Multiply the third equation by 2: 2(5x + 9y) = 2(5) 10x + 18y = 10

Now, subtract the third equation from the second equation: (10x + 18y) - (3x + 5y) = 10 - 1 10x + 18y - 3x - 5y = 9 7x + 13y = 9 ----(5)

We now have a system of two equations: x + y = -3 ----(4) 7x + 13y = 9 ----(5)

To solve this system, we can multiply equation (4) by 7 and equation (5) by 1 to eliminate x:

7(x + y) = 7(-3) 7x + 7y = -21

1(7x + 13y) = 1(9) 7x + 13y = 9

Now, subtract the first equation from the second equation: (7x + 13y) - (7x + 7y) = 9 - (-21) 7x + 13y - 7x - 7y = 9 + 21 6y = 30 y = 30/6 y = 5

Substitute the value of y into equation (4) to find x: x + 5 = -3 x = -3 - 5 x = -8

Therefore, the solution to the second system of equations is: x = -8 y = 5

Conclusion:

The solutions to the given systems of equations are:

System 1: x = 4.33 y = -4.5

System 2: x = -8 y = 5

Please let me know if you need any further assistance!