Solve the System of Linear Equations: x + y = 10 and 2x - y = 2

1. Add the two equations to eliminate :

2. Solve for :

3. Substitute back into the first equation to solve for :

## Solution to the System of Equations

To solve the system of equations:

$$
\begin{cases}
x + y = 10 \\
2x - y = 2
\end{cases}
$$

we can use the method of substitution or elimination. Here, we'll use the elimination method.

1. **Add the two equations to eliminate \( y \):**

$$
(x + y) + (2x - y) = 10 + 2
$$

$$
x + y + 2x - y = 12
$$

$$
3x = 12
$$

2. **Solve for \( x \):**

$$
x = \frac{12}{3} = 4
$$

3. **Substitute \( x = 4 \) back into the first equation to solve for \( y \):**

$$
x + y = 10
$$

$$
4 + y = 10
$$

$$
y = 10 - 4
$$

$$
y = 6
$$

Thus, the solution to the system of equations is:

$$
(x, y) = (4, 6)