We are asked to solve the following system of equations using the substitution method: $2x - y = 2$ $5x + 6y = 8$

1. Problem Description

We are asked to solve the following system of equations using the substitution method:

$2x - y = 2$

$5x + 6y = 8$

2. Solution Steps

First, solve the first equation for $y$:

$2x - y = 2$

$y = 2x - 2$

Next, substitute this expression for $y$ into the second equation:

$5x + 6y = 8$

$5x + 6(2x - 2) = 8$

$5x + 12x - 12 = 8$

$17x = 20$

$x = \frac{20}{17}$

Now, substitute $x = \frac{20}{17}$ back into the equation $y = 2x - 2$:

$y = 2(\frac{20}{17}) - 2$

$y = \frac{40}{17} - \frac{34}{17}$

$y = \frac{6}{17}$

3. Final Answer

The solution is $(x, y) = (\frac{20}{17}, \frac{6}{17})$.