$$ \begin{array}{l} =m(x+y)+n(x+y) \ -(x+y)(m+n) \ \text { a }+x-2 y+b z-b y \ = \ 7 \ \text { 3. } a x+a y+b x-b y \ =a(x+y)-b(z+y) \ =(x-y)(a-b) \ \text { 4. } a+b-a x-b= \ = \ 7 \ \text { 5. } a-0+a b-1= \ 7 \end{array} $$

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Let's analyze the given equations step by step and extract the known conditions.

### Step 1: Extract Known Conditions

1. **Equation 1:**
   $$
   m(x+y) + n(x+y) - (x+y)(m+n) = 0
   $$
   This simplifies to $$0 = 0$$, which is always true.

2. **Equation 2:**
   $$
   a + x - 2y + bz - by = 7
   $$

3. **Equation 3:**
   $$
   ax + ay + bx - by = a(x+y) - b(z+y) = (x-y)(a-b)
   $$

4. **Equation 4:**
   $$
   a + b - ax - b = 7
   $$
   This simplifies to:
   $$
   a - ax = 7 \implies a(1-x) = 7
   $$

5. **Equation 5:**
   $$
   a - 0 + ab - 1 = 7
   $$
   This simplifies to:
   $$
   a + ab - 1 = 7 \implies a + ab = 8
   $$

### Step 2: Solve the Equations

Now we have the following equations to solve:

1. $$ a(1-x) = 7 $$  (Equation 4)
2. $$ a + ab = 8 $$   (Equation 5)

From Equation 4, we can express $$ a $$ in terms of $$ x $$:
$$
a = \frac{7}{1-x}
$$

Substituting this expression for $$ a $$ into Equation 5:
$$
\frac{7}{1-x} + \frac{7}{1-x}b = 8
$$

Multiplying through by $$ 1-x $$ to eliminate the fraction:
$$
7 + 7b = 8(1-x)
$$
$$
7 + 7b = 8 - 8x
$$
Rearranging gives:
$$
7b + 8x = 1
$$

Now we have a new equation:
1. $$ 7b + 8x = 1 $$  (Equation 6)

### Step 3: Solve for $$ b $$ and $$ x $$

We can express $$ b $$ in terms of $$ x $$:
$$
b = \frac{1 - 8x}{7}
$$

Now we can substitute this back into any of the previous equations to find specific values for $$ a $$, $$ b $$, and $$ x $$.

### Step 4: Substitute $$ b $$ into Equation 5

Substituting $$ b $$ into $$ a + ab = 8 $$:
$$
a + a\left(\frac{1 - 8x}{7}\right) = 8
$$
Substituting $$ a = \frac{7}{1-x} $$:
$$
\frac{7}{1-x} + \frac{7}{1-x}\left(\frac{1 - 8x}{7}\right) = 8
$$
This simplifies to:
$$
\frac{7}{1-x} + \frac{1 - 8x}{1-x} = 8
$$
Combining the fractions:
$$
\frac{7 + 1 - 8x}{1-x} = 8
$$
$$
\frac{8 - 8x}{1-x} = 8
$$
Cross-multiplying gives:
$$
8 - 8x = 8(1-x)
$$
Expanding:
$$
8 - 8x = 8 - 8x
$$
This is always true, indicating that $$ a $$ and $$ b $$ can take on multiple values depending on $$ x $$.

### Conclusion

The system of equations does not yield unique values for $$ a $$, $$ b $$, and $$ x $$ but rather a relationship among them. The values can be expressed in terms of one variable, such as $$ x $$.

If you have specific values or constraints for $$ x $$, we can find corresponding values for $$ a $$ and $$ b $$.
The equations show that $$ a $$ and $$ b $$ are related to $$ x $$ by the equations $$ a = \frac{7}{1-x} $$ and $$ b = \frac{1 - 8x}{7} $$. Without additional information, multiple solutions exist depending on the value of $$ x $$.

\[ \begin{array}{l} =m(x+y)+n(x+y) \\ -(x+y)(m+n) \\ \text { a }+x-2 y+b z-b y \\ = \\ 7 \\ \text { 3. } a x+a y+b x-b y \\ =a(x+y)-b(z+y) \\ =(x-y)(a-b) \\ \text { 4. } a+b-a x-b= \\ = \\ 7 \\ \text { 5. } a-0+a b-1= \\ 7 \end{array} \]

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