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To solve the system of equations:

1. \( 2x - y = -1 \)
2. \( x + y = 10 \)

You can use either substitution or elimination. Here, I'll use substitution:

1. From the second equation, solve for \( y \): \[ y = 10 - x \]

2. Substitute \( y = 10 - x \) into the first equation: \[ 2x - (10 - x) = -1 \]

3. Simplify and solve for \( x \): \[ 2x - 10 + x = -1 \] \[ 3x - 10 = -1 \] \[ 3x = 9 \] \[ x = 3 \]

4. Substitute \( x = 3 \) back into \( y = 10 - x \): \[ y = 10 - 3 = 7 \]

The solution to the system of equations is \( x = 3 \) and \( y = 7 \).