Solve the system of equations by using substitution.

- 9 = x - 3 y

- 2 x + 6 = 6 y

A. (3, 4)

B. infinitely many solutions

C. (-9, 0)

D. (-3, 2)

x = - 3, y = 2 thus D) is your answer

Step-by-step explanation by substitution:

Solve the following system:

{-9 = x - 3 y

6 - 2 x = 6 y

Hint: | Choose an equation and a variable to solve for.

In the first equation, look to solve for x:

{-9 = x - 3 y

6 - 2 x = 6 y

Hint: | Reverse the equality in - 9 = x - 3 y in order to isolate x to the left hand side.

-9 = x - 3 y is equivalent to x - 3 y = - 9:

{x - 3 y = - 9

6 - 2 x = 6 y

Hint: | Solve for x.

Add 3 y to both sides:

{x = 3 y - 9

6 - 2 x = 6 y

Hint: | Perform a substitution.

Substitute x = 3 y - 9 into the second equation:

{x = 3 y - 9

6 - 2 (3 y - 9) = 6 y

Hint: | Expand the left hand side of the equation 6 - 2 (3 y - 9) = 6 y.

6 - 2 (3 y - 9) = (18 - 6 y) + 6 = 24 - 6 y:

{x = 3 y - 9

24 - 6 y = 6 y

Hint: | Choose an equation and a variable to solve for.

In the second equation, look to solve for y:

{x = 3 y - 9

24 - 6 y = 6 y

Hint: | Isolate y to the left hand side.

Subtract 6 y + 24 from both sides:

{x = 3 y - 9

-12 y = - 24

Hint: | Solve for y.

Divide both sides by - 12:

{x = 3 y - 9

y = 2

Hint: | Perform a back substitution.

Substitute y = 2 into the first equation:

Answer: {x = - 3, y = 2