How many solutions exist for the system of equations below?
(3x+y=18
(3x+y=16
none
one
two
infinitely many
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No solution exists for the given system of equations.

Step-by-step explanation:

The given system of equation are :

3x+y=18  (1)

3x+y=16  (2)

Comparing the two equations (1) and (2), it can be determined that :

The solution set for the system of equation is (x,y).

Since the given equations cannot be solved for x and y values, The system has NO SOLUTION.

Therefore, the option a) none is the solution of given system of equations.

step-by-step explanation:

which of the following statements correctly describes the expression below based on its degree and number of terms?

314 - 7x2 + 11

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°