According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:

c² = a² + b²
c² = 8² + 1²
c² = 64 + 1
c² = 65
c = \( \sqrt{65} \)

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

-8c + y = -2
y = -2 + 8c

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

-9c + 5(-2 + 8c) = -6
-9c + (5 x -2) + (5 x 8c) = -6
-9c - 10 + 40c = -6
-9c + 40c = -6 + 10
31c = 4
c = \( \frac{4}{31} \)
c = \(\frac{4}{31}\)

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 -24 as well and sum (Inside, Outside) to equal -5. For this problem, those two numbers are -8 and 3. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² - 5y - 24
y² + (-8 + 3)y + (-8 x 3)
(y - 8)(y + 3)

A circle is a figure in which each point around its perimeter is an equal distance from the center. The radius of a circle is the distance between the center and any point along its perimeter. A chord is a line segment that connects any two points along its perimeter. The diameter of a circle is the length of a chord that passes through the center of the circle and equals twice the circle's radius (2r).

The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:

c² + 2c - 1 = -2c + 4
c² + 2c - 1 - 4 = -2c
c² + 2c + 2c - 5 = 0
c² + 4c - 5 = 0

Next, factor the quadratic equation:

c² + 4c - 5 = 0
(c - 1)(c + 5) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (c - 1) or (c + 5) must equal zero:

If (c - 1) = 0, c must equal 1
If (c + 5) = 0, c must equal -5

So the solution is that c = 1 or -5