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.

-6a - 3 = \( \frac{a}{7} \)
7 x (-6a - 3) = a
(7 x -6a) + (7 x -3) = a
-42a - 21 = a
-42a - 21 - a = 0
-42a - a = 21
-43a = 21
a = \( \frac{21}{-43} \)
a = -\(\frac{21}{43}\)

An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite:

d° = b° + c°

To find angle c, remember that the sum of the interior angles of a triangle is 180°:

180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 63° - 66° = 51°

So, d° = 66° + 51° = 117°

A shortcut to get this answer is to remember that angles around a line add up to 180°:

a° + d° = 180°
d° = 180° - a°
d° = 180° - 63° = 117°

You need to find the value of b so solve the first equation in terms of y:

8b + y = -2
y = -2 - 8b

then substitute the result (-2 - 8b) into the second equation:

-7b + 8(-2 - 8b) = 5
-7b + (8 x -2) + (8 x -8b) = 5
-7b - 16 - 64b = 5
-7b - 64b = 5 + 16
-71b = 21
b = \( \frac{21}{-71} \)
b = -\(\frac{21}{71}\)

To factor a quadratic expression, apply the FOIL method (First, Outside, Inside, Last) in reverse. First, find the two Last terms that will multiply to produce -16 as well and sum (Inside, Outside) to equal -6. For this problem, those two numbers are -8 and 2. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² - 6y - 16
y² + (-8 + 2)y + (-8 x 2)
(y - 8)(y + 2)

When solving an equation with two variables, replace the variables with the values given and then solve the now variable-free equation. (Remember order of operations, PEMDAS, Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.)