Solve x + y = 10 and x - y = 4.

Answer

To solve the system of equations \( x + y = 10 \) and \( x - y = 4 \), we can use the substitution method. Here’s a step-by-step solution:

### Step 1: Identify the equations
We have two equations:
1. \( x + y = 10 \) (Equation 1)
2. \( x - y = 4 \) (Equation 2)

### Step 2: Solve one equation for one variable
Let's solve Equation 1 for \( x \):
\[ x = 10 - y \]
We will call this Equation 3.

### Step 3: Substitute the value of \( x \) into the second equation
Now, we substitute the value of \( x \) from Equation 3 into Equation 2:
\[ (10 - y) - y = 4 \]

### Step 4: Simplify the equation
Combine like terms:
\[ 10 - y - y = 4 \\ 10 - 2y = 4 \]

### Step 5: Solve for \( y \)
Now, isolate \( y \):
\[ -2y = 4 - 10 \\ -2y = -6 \\ y = \frac{-6}{-2} \\ y = 3 \]

### Step 6: Substitute \( y \) back to find \( x \)
Now that we have \( y \), substitute it back into Equation 1 to find \( x \):
\[ x + 3 = 10 \\ x = 10 - 3 \\ x = 7 \]

### Final Solution
The solution to the system of equations is:
\[ x = 7, \quad y = 3 \]