The area of a triangle is equal to ½ base x height:

a = ½bh
a = ½ x 1 x 1 = \( \frac{1}{2} \) = \(\frac{1}{2}\)

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

-3c + y = -4
y = -4 + 3c

then substitute the result (-4 - -3c) into the second equation:

-6c - 5(-4 + 3c) = 5
-6c + (-5 x -4) + (-5 x 3c) = 5
-6c + 20 - 15c = 5
-6c - 15c = 5 - 20
-21c = -15
c = \( \frac{-15}{-21} \)
c = \(\frac{5}{7}\)

An equation is two expressions separated by an equal sign. The key to solving equations is to 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.

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 -10 as well and sum (Inside, Outside) to equal -3. For this problem, those two numbers are -5 and 2. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² - 3y - 10
y² + (-5 + 2)y + (-5 x 2)
(y - 5)(y + 2)

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

c² = a² + b²
c² = 7² + 1²
c² = 49 + 1
c² = 50
c = \( \sqrt{50} \)