You need to find the value of c so solve the first equation in terms of x:

c + x = -4
x = -4 - c

then substitute the result (-4 - 1c) into the second equation:

-6c + 4(-4 - c) = 8
-6c + (4 x -4) + (4 x -c) = 8
-6c - 16 - 4c = 8
-6c - 4c = 8 + 16
-10c = 24
c = \( \frac{24}{-10} \)
c = -2\(\frac{2}{5}\)

For parallel lines with a transversal, the following relationships apply:

• angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°)
• alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°)
• 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°)

Applying these relationships starting with b° = 165, the value of w° is 15.

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 + 5)(y - 8)
(y x y) + (y x -8) + (5 x y) + (5 x -8)
y² - 8y + 5y - 40
y² - 3y - 40

To solve this equation, isolate the variable for which you are solving (b) on one side of the equation and put everything else on the other side.

-b + 5y = -8b + 9y - 3
-b = -8b + 9y - 3 - 5y
-b + 8b = 9y - 3 - 5y
7b = 4y - 3
b = \( \frac{4y - 3}{7} \)
b = \( \frac{4y}{7} \) + \( \frac{-3}{7} \)
b = \(\frac{4}{7}\)y - \(\frac{3}{7}\)

A parallelogram is a quadrilateral with two sets of parallel sides. Opposite sides (a = c, b = d) and angles (red = red, blue = blue) are equal. The area of a parallelogram is base x height and the perimeter is the sum of the lengths of all sides (a + b + c + d).