find the values of x,y and zfrom the following equations :
`(i) [{:(4,3),(x,5):}]=[{:(y,z),(1,5):}]`
`(ii) [{:(x+y,2),(5+z,xy):}]=[{:(6,2),(5,8):}]`
`(iii) [{:(x+y+z),(x+z),(y+z):}]=[{:(9),(5),(7):}]`

Explanation

To solve for the values of \(x\), \(y\), and \(z\) from the given equations, we will analyze each equation step by step.

### Given Equations:
1. \(\begin{pmatrix} 4 & 3 \\ x & 5 \end{pmatrix} = \begin{pmatrix} y & z \\ 1 & 5 \end{pmatrix}\)
2. \(\begin{pmatrix} x+y & 2 \\ 5+z & xy \end{pmatrix} = \begin{pmatrix} 6 & 2 \\ 5 & 8 \end{pmatrix}\)
3. \(\begin{pmatrix} x+y+z & x+z & y+z \end{pmatrix} = \begin{pmatrix} 9 \\ 5 \\ 7 \end{pmatrix}\)

### Step 1: Solve the First Equation
From the first equation, we equate the corresponding elements of the matrices:

- \(4 = y\)
- \(3 = z\)
- \(x = 1\)

Thus, we have:
- \(y = 4\)
- \(z = 3\)
- \(x = 1\)

### Step 2: Solve the Second Equation
Using the values of \(x\) and \(y\) from Step 1, we substitute \(x = 1\) and \(y = 4\) into the second equation:

\[ \begin{pmatrix} 1 + 4 & 2 \\ 5 + z & 1 \cdot 4 \end{pmatrix} = \begin{pmatrix} 6 & 2 \\ 5 & 8 \end{pmatrix} \]

This gives us:
- \(1 + 4 = 6\) (which is correct)
- \(2 = 2\) (which is correct)
- \(5 + z = 5\) implies \(z = 0\) (which contradicts our earlier value of \(z\))
- \(1 \cdot 4 = 8\) implies \(4 = 8\) (which is incorrect)

Since we have a contradiction, we need to re-evaluate our values of \(x\), \(y\), and \(z\).

### Step 3: Solve the Third Equation
Now, let's analyze the third equation:

\[ \begin{pmatrix} x+y+z & x+z & y+z \end{pmatrix} = \begin{pmatrix} 9 \\ 5 \\ 7 \end{pmatrix} \]

From this, we get the following equations:
1. \(x + y + z = 9\)
2. \(x + z = 5\)
3. \(y + z = 7\)

### Step 4: Substitute and Solve
From the second equation, we can express \(x\) in terms of \(z\):
\[ x = 5 - z \]

Now substitute \(x\) into the first equation:
\[ (5 - z) + y + z = 9 \]
This simplifies to:
\[ 5 + y = 9 \implies y = 4 \]

Now, substitute \(y\) into the third equation:
\[ 4 + z = 7 \implies z = 3 \]

Finally, substitute \(z\) back into the expression for \(x\):
\[ x = 5 - 3 = 2 \]

### Final Values
Thus, the values are:
- \(x = 2\)
- \(y = 4\)
- \(z = 3\)

### Summary of the Solution:
- \(x = 2\)
- \(y = 4\)
- \(z = 3\)