Question

If x + 2y = 9 and 3x - y = -8, what is the value of (2x+y)?

Answer 1

To find the value of (2x+y), we need to solve the given system of equations. By performing the elimination method on the equations, we obtain the values x = -1 and y = 5. Substituting these values into (2x+y), we find that the value is 3.

Step-by-step explanation:

To find the value of (2x+y), we need to first solve the given system of equations.

The given equations are:

x + 2y = 9 ...........(1)

3x - y = -8 ...........(2)

We can solve this system of equations by substitution or elimination method.

Using the elimination method, we can multiply equation (1) by 3 and equation (2) by 2 to eliminate y:

3(x + 2y) = 3(9) => 3x + 6y = 27 ...........(3)

2(3x - y) = 2(-8) => 6x - 2y = -16 ...........(4)

Now, let's add equations (3) and (4):

(3x + 6y) + (6x - 2y) = 27 + (-16)

9x + 4y = 11 ...........(5)

We can solve equations (2) and (5) to find the values of x and y:

3x - y = -8 ...........(2)

9x + 4y = 11 ...........(5)

Multiplying equation (2) by 4 and equation (5) by 1, we can eliminate y:

4(3x - y) = 4(-8) => 12x - 4y = -32 ...........(6)

1(9x + 4y) = 1(11) => 9x + 4y = 11 ...........(7)

Now, let's add equations (6) and (7):

(12x - 4y) + (9x + 4y) = -32 + 11

21x = -21

x = -1

Substituting the value of x in equation (2):

3(-1) - y = -8

-3 - y = -8

-y = -8 + 3

-y = -5

y = 5

Now, we can find the value of (2x+y):

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

Answer 2

The value of (2x+y) is 3.

Step-by-step explanation:

First, we have to find the values of x and y.

We have that:

x + 2y = 9, which also means that:

x = 9 - 2y

Replacing into the second equation, to find y:

`3x - y = -8`

`3(9 - 2y) - y = -8`

`27 - 6y - y = -8`

`7y = 35`

`y = (35)/(7)`

`y = 5`

Finding x:

`x = 9 - 2y = 9 - 10 = -1`

What is the value of (2x+y)?

2(-1) + 5 = -2 + 5 = 3

The value of (2x+y) is 3.