The solution of the pair of equation `(x)/(2) + y = 0.8 and x + (y)/(2) = (7)/(10),` is

Options

A. `x = (2)/(5), y = (3)/(5)`
B. `x = (2)/(3) , y = 5`
C. `x = (2)/(5) , y = (5)/(3)`
D. `x = (3)/(5), y = (2)/(5)`

Answer

To solve the pair of equations given by:

1. \(\frac{x}{2} + y = 0.8\)
2. \(x + \frac{y}{2} = \frac{7}{10}\)

we will follow these steps:

### Step 1: Rewrite the equations
First, we can rewrite the equations for clarity:

1. \(\frac{x}{2} + y = 0.8\) can be rewritten as \(\frac{x}{2} + y = \frac{8}{10}\).
2. The second equation remains as \(x + \frac{y}{2} = \frac{7}{10}\).

### Step 2: Eliminate fractions by multiplying
Next, we will eliminate the fractions by multiplying the first equation by 10 and the second equation by 20:

1. Multiply the first equation by 10:
\[ 10 \left(\frac{x}{2} + y\right) = 10 \cdot \frac{8}{10} \]
This simplifies to:
\[ 5x + 10y = 8 \quad \text{(Equation 1)} \]

2. Multiply the second equation by 20:
\[ 20 \left(x + \frac{y}{2}\right) = 20 \cdot \frac{7}{10} \]
This simplifies to:
\[ 20x + 10y = 14 \quad \text{(Equation 2)} \]

### Step 3: Set up the equations for elimination
Now we have the two equations:
1. \(5x + 10y = 8\)
2. \(20x + 10y = 14\)

### Step 4: Subtract the equations
Next, we will subtract Equation 1 from Equation 2 to eliminate \(y\):
\[ (20x + 10y) - (5x + 10y) = 14 - 8 \]
This simplifies to:
\[ 15x = 6 \]

### Step 5: Solve for \(x\)
Now, we can solve for \(x\):
\[ x = \frac{6}{15} = \frac{2}{5} \]

### Step 6: Substitute \(x\) back to find \(y\)
Now that we have \(x\), we can substitute it back into either equation to find \(y\). We will use Equation 1:
\[ 5\left(\frac{2}{5}\right) + 10y = 8 \]
This simplifies to:
\[ 2 + 10y = 8 \]
Subtracting 2 from both sides gives:
\[ 10y = 6 \]
Thus,
\[ y = \frac{6}{10} = \frac{3}{5} \]

### Final Solution
The solution to the system of equations is:
\[ \left(x, y\right) = \left(\frac{2}{5}, \frac{3}{5}\right) \]