Solve for x and y, x + y = 2, x - y = 1

Answer

To solve the equations \( x + y = 2 \) and \( x - y = 1 \), we can follow these steps:

### Step 1: Write down the equations
We have two equations:
1. \( x + y = 2 \) (Equation 1)
2. \( x - y = 1 \) (Equation 2)

### Step 2: Add the two equations
To eliminate \( y \), we can add Equation 1 and Equation 2:
\[ (x + y) + (x - y) = 2 + 1 \]
This simplifies to:
\[ 2x = 3 \]

### Step 3: Solve for \( x \)
Now, divide both sides by 2 to find \( x \):
\[ x = \frac{3}{2} \]

### Step 4: Substitute \( x \) back into one of the original equations
Now that we have \( x \), we can substitute it back into Equation 1 to find \( y \):
\[ \frac{3}{2} + y = 2 \]

### Step 5: Solve for \( y \)
To isolate \( y \), subtract \( \frac{3}{2} \) from both sides:
\[ y = 2 - \frac{3}{2} \]
To perform the subtraction, convert 2 into a fraction:
\[ y = \frac{4}{2} - \frac{3}{2} = \frac{1}{2} \]

### Final Solution
Thus, the solution to the equations is:
\[ x = \frac{3}{2}, \quad y = \frac{1}{2} \]