What is the value of y in the solution to the system of equations? x + y = 12x – 3y = –30

There are three possibilities for the given question,

Case 1 : if question is,

x + y = 12 -----(1) ; x - 3y = - 30 -----(2),

Subtraction equation (1) and Equation (2),

We get,

4y = 42

Case 2 :

If the equations are,

x + y = 1 ----(1);  2x - 3y = -30-----(2),

Equation (2) - 2 × Equation (1),

We get,

-5y = -32

Case 3 :

if the equations are,

x + y = 12x - 3y = - 30

⇒ x + y = - 30 ------(1)

And, 12x - 3y = - 30 ------(2)

Equation (2) - 12 × Equation (1),

We get,

-3y - 12y = - 30 + 360

⇒ - 15 y = 330

Dividing both sides by - 15,

⇒ y = -22

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°