#### Answer

$$y = 0$$
To check if this solution is correct, we substitute $0$ in for $y$:
$$6(0 - 1) + 7 = 9(0) - 0 + 1$$
Simplify what is in parentheses first:
$$-6 + 7 - 0 = 0 + 1$$
Subtract or add from left to right:
$$1 - 0 = 1$$
Simplify:
$$1 = 1$$
Since both sides of the equation equal one another, we know that the solution is correct.

#### Work Step by Step

First, we need to simplify this equation.
Distribute terms that are in parentheses:
$$6y - 6 + 7 = 9y - y +1$$
Next, combine like terms on both sides of the equation:
$$6y + 1 = 8y + 1$$
Move variables to one side of the equation:
$$2y + 1 = 1$$
Subtract each side by $1$ to move constants to one side of the equation:
$$2y = 0$$
Divide each side by $2$ to isolate $y$:
$$y = 0$$
To check if this solution is correct, we substitute $0$ in for $y$:
$$6(0 - 1) + 7 = 9(0) - 0 + 1$$
Simplify what is in parentheses first:
$$-6 + 7 - 0 = 0 + 1$$
Subtract or add from left to right:
$$1 - 0 = 1$$
Simplify:
$$1 = 1$$
Since both sides of the equation equal one another, we know that the solution is correct.