Introductory Algebra for College Students (7th Edition)

$$y = 0$$ 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.
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.