To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the equal sign and the answer on the other.

4y + 1 = \( \frac{y}{8} \)
8 x (4y + 1) = y
(8 x 4y) + (8 x 1) = y
32y + 8 = y
32y + 8 - y = 0
32y - y = -8
31y = -8
y = \( \frac{-8}{31} \)
y = -\(\frac{8}{31}\)

Parallel lines are lines that share the same slope (steepness) and therefore never intersect. A transversal occurs when a set of parallel lines are crossed by another line. All of the angles formed by a transversal are called interior angles and angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°) and are called corresponding angles. Alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°) and all acute angles (a° = c° = w° = z°) and all obtuse angles (b° = d° = x° = y°) equal each other. Same-side interior angles are supplementary and add up to 180° (e.g. a° + d° = 180°, d° + c° = 180°).

To multiply binomials, use the FOIL method. FOIL stands for First, Outside, Inside, Last and refers to the position of each term in the parentheses:

(y - 8)(y - 8)
(y x y) + (y x -8) + (-8 x y) + (-8 x -8)
y² - 8y - 8y + 64
y² - 16y + 64

To multiply monomials, multiply the coefficients (the numbers that come before the variables) of each term, add the exponents of like variables, and multiply the different variables together.

(7a)(2ab) + (9a²)(3b)
(7 x 2)(a x a x b) + (9 x 3)(a² x b)
(14)(a¹⁺¹ x b) + (27)(a²b)
14a²b + 27a²b
41a²b

To combine like terms, add or subtract the coefficients (the numbers that come before the variables) of terms that have the same variable raised to the same exponent.

6a⁴ - 2a⁴ = 4a⁴