If `(x+y)/(x-y)=5/3` and `x/(y+2)=2`, then the value of (x,y) is

Options

A. (4,1)
B. (2,8)
C. (1,4)
D. (8,2)

Answer

To solve the equations given in the problem, we will follow these steps:

### Step 1: Start with the first equation
We have the equation:
\[ \frac{x+y}{x-y} = \frac{5}{3} \]
Cross-multiply to eliminate the fraction:
\[ 3(x+y) = 5(x-y) \]

### Step 2: Expand both sides
Expanding both sides gives:
\[ 3x + 3y = 5x - 5y \]

### Step 3: Rearrange the equation
Rearranging the equation to group like terms:
\[ 3x + 3y - 5x + 5y = 0 \]
This simplifies to:
\[ -2x + 8y = 0 \]
or
\[ 2x = 8y \]
Dividing both sides by 2:
\[ x = 4y \]

### Step 4: Substitute into the second equation
Now we use the second equation:
\[ \frac{x}{y+2} = 2 \]
Substituting \(x = 4y\) into this equation:
\[ \frac{4y}{y+2} = 2 \]

### Step 5: Cross-multiply again
Cross-multiplying gives:
\[ 4y = 2(y + 2) \]

### Step 6: Expand and simplify
Expanding the right side:
\[ 4y = 2y + 4 \]
Rearranging gives:
\[ 4y - 2y = 4 \]
This simplifies to:
\[ 2y = 4 \]
Dividing both sides by 2:
\[ y = 2 \]

### Step 7: Find the value of x
Now substituting \(y = 2\) back into \(x = 4y\):
\[ x = 4(2) = 8 \]

### Final Result
Thus, the values of \(x\) and \(y\) are:
\[ (x, y) = (8, 2) \]

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