If ` z= (4x-5y)/(5x- 4y)` , then express x in terms of y and z.

Answer

To express \( x \) in terms of \( y \) and \( z \) from the equation \( z = \frac{4x - 5y}{5x - 4y} \), we can follow these steps:

### Step 1: Write down the given equation
We start with the equation:
\[ z = \frac{4x - 5y}{5x - 4y} \]

### Step 2: Cross-multiply
To eliminate the fraction, we cross-multiply:
\[ z(5x - 4y) = 4x - 5y \]

### Step 3: Distribute \( z \) on the left side
Now, distribute \( z \) on the left side:
\[ 5zx - 4zy = 4x - 5y \]

### Step 4: Rearrange the equation
Next, we want to get all terms involving \( x \) on one side and the other terms on the opposite side. We can rearrange it as follows:
\[ 5zx - 4x = 4zy - 5y \]

### Step 5: Factor out \( x \)
Now, factor \( x \) out from the left side:
\[ x(5z - 4) = 4zy - 5y \]

### Step 6: Solve for \( x \)
Finally, divide both sides by \( (5z - 4) \) to isolate \( x \):
\[ x = \frac{4zy - 5y}{5z - 4} \]

### Final Expression
Thus, the expression for \( x \) in terms of \( y \) and \( z \) is:
\[ x = \frac{y(4z - 5)}{5z - 4} \]

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