if x+y=7,y+z=4,x+z=3.what is x+y+z.and find the value of each

We are given three equations:

1. \( x + y = 7 \)
2. \( y + z = 4 \)
3. \( x + z = 3 \)

To find \( x + y + z \), we can add all three equations:

\[
(x + y) + (y + z) + (x + z) = 7 + 4 + 3
\]
\[
2x + 2y + 2z = 14
\]

Now, divide both sides by 2:

\[
x + y + z = 7
\]

So, \( x + y + z = 7 \).

### Solving for \( x \), \( y \), and \( z \):

We now know that \( x + y + z = 7 \). Using this, we can substitute into the original equations.

#### Step 1: Solve for \( x \)

From equation \( x + z = 3 \), and knowing \( x + y + z = 7 \), we can express \( y \) as:
\[
y = 7 - (x + z) = 7 - 3 = 4
\]

#### Step 2: Solve for \( z \)

Substitute \( y = 4 \) into the second equation \( y + z = 4 \):
\[
4 + z = 4
\]
\[
z = 0
\]

#### Step 3: Solve for \( x \)

Substitute \( z = 0 \) into the third equation \( x + z = 3 \):
\[
x + 0 = 3
\]
\[
x = 3
\]

### Final values:

- \( x = 3 \)
- \( y = 4 \)
- \( z = 0 \)

Would you like further details or have any questions?

Here are 5 related questions to practice:

1. If \( x - y = 2 \) and \( y + z = 6 \), what is \( x + z \)?
2. Solve for \( x \), \( y \), and \( z \) if \( x + 2y = 8 \), \( y + z = 5 \), and \( z - x = 1 \).
3. What is the sum of \( x + y + z \) if \( x = 4 \), \( y = -2 \), and \( z = 5 \)?
4. If \( x + y = 10 \), \( y + z = 12 \), and \( z + x = 8 \), find \( x \), \( y \), and \( z \).
5. Solve the system: \( 2x + 3y = 13 \), \( x - y = 2 \).

**Tip**: When solving systems of linear equations, adding or subtracting equations can help simplify and eliminate variables quickly.

If x + y = 7, y + z = 4, x + z = 3. What is x + y + z and find the value of each?

Learn how to solve a system of linear equations with three variables: x + y = 7, y + z = 4, and x + z = 3. This step-by-step guide covers key algebraic concepts, such as adding equations to eliminate variables and using substitution to find the values of x, y, and z. Suitable for students in Grades 8-10.

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