Write the value `x-y+z` from the following equation :
`[(x+y+z),(x+z),(y+z)]=[(9),(5),(7)]`

Answer

To find the value of \( x - y + z \) from the given equations, we start with the equality of the two matrices:

\[ [(x+y+z),(x+z),(y+z)] = [(9),(5),(7)] \]

This gives us three equations:

1. \( x + y + z = 9 \) (Equation 1)
2. \( x + z = 5 \) (Equation 2)
3. \( y + z = 7 \) (Equation 3)

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

From Equation 2, we can express \( x \) in terms of \( z \):

\[ x = 5 - z \tag{4} \]

### Step 2: Substitute \( x \) into Equation 1

Now, substitute Equation 4 into Equation 1:

\[ (5 - z) + y + z = 9 \]

Simplifying this gives:

\[ 5 + y = 9 \]

So,

\[ y = 9 - 5 = 4 \tag{5} \]

### Step 3: Substitute \( y \) into Equation 3

Now that we have \( y \), we can substitute it into Equation 3 to find \( z \):

\[ 4 + z = 7 \]

This simplifies to:

\[ z = 7 - 4 = 3 \tag{6} \]

### Step 4: Substitute \( z \) back to find \( x \)

Now we can substitute the value of \( z \) back into Equation 4 to find \( x \):

\[ x = 5 - 3 = 2 \tag{7} \]

### Step 5: Calculate \( x - y + z \)

Now that we have \( x \), \( y \), and \( z \):

- \( x = 2 \)
- \( y = 4 \)
- \( z = 3 \)

We can find \( x - y + z \):

\[ x - y + z = 2 - 4 + 3 \]

Calculating this gives:

\[ = 2 - 4 + 3 = 1 \]

Thus, the value of \( x - y + z \) is:

\[ \boxed{1} \]