Question

X+y+2z=4; 2x+y-2z=7; 3x+y+2z=6

Answer 1

Ответ:

вот сделал с photomath .

Answer 2

You have a system of three linear equations with three variables (x, y, and z):

1. x + y + 2z = 4
2. 2x + y - 2z = 7
3. 3x + y + 2z = 6

To solve this system of equations, you can use either the substitution method or the elimination method. Here, I'll use the elimination method:

First, let's add equations (1) and (3) to eliminate the variable z:

1. x + y + 2z = 4
2. 3x + y + 2z = 6

Adding them:

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

Now, divide the entire equation by 2 to simplify it:

2x + y + 2z = 5

So, you have the following simplified system:

1. x + y + 2z = 4
2. 2x + y - 2z = 7
3. 2x + y + 2z = 5

Now, you can subtract equation (2) from equation (4) to eliminate z:

4. (2x + y + 2z) - (2x + y - 2z) = 5 - 7

This simplifies to:

4z = -2

Now, divide both sides by 4:

z = -2/4 z = -1/2

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

1. x + y + 2z = 4 x + y + 2(-1/2) = 4 x + y - 1 = 4

Add 1 to both sides:

x + y = 4 + 1 x + y = 5

Now, you have:

x + y = 5

So, you've solved for x, y, and z:

x = 5 - y z = -1/2

These are the solutions to your system of equations, and you can express them as a set of equations:

x = 5 - y y can take any value. z = -1/2