Y + X = 0, 3y + 6x = -9

Y + x = 0
3y + 6x = -9

 

Answer:

x = -3 and y = 3

Step-by-step explanation:

Linear system:

Equation (1):

x + y = 0

y = -x

Equation (2):

3y + 6x = -9

Solution by substitution, y = -x:

3y + 6x = -9

3(-x) + 6x = -9

-3x + 6x = -9

3x/3 = -9/3

x = -3

Find y when x = -3:

y + x = 0

y + (-3) = 0

y = 3

The solution to the linear system:

x = -3 and y = 3

Properties of the linear system:

a) Intersecting lines at Point (-3, 3)

b.) The system is independent and consistent.

c.) There is only one solution (x,y) = (-3, 3)

Check:

Equation (1):

x + y = 0

(-3) + (3) = 0

0 = 0  (True)

Equation (2):

3y + 6x = -9

3(3) + 6(-3) = -9

9 - 18 = -9

-9 = -9  (True)