Solve the system of equations by the substitution method.?

Question

{3y = x + 54
{2x + 6y = 0

a. (9, -27)
b. ( -27, 9)
c. infinite number of solutions
d. no solution

Answer 1

3y=x+54
divide both sides by 3
y=(x+54)/3
substitute into the other equation(2x+6y=0)
2x+6((x+54)/3)=0
simplify
-2x=2x+108
simplify
-4x=108
x=-27
substitute -27 into either equation(3y=x+54 or 2x+6y=0)
y=9
SOLUTION= b. (-27,9)

Answer 2

Substitution Method

3y = x + 54- - - - - Equation 1
2x + 6y = 0- - - - - Equation 2
- - - - - - - - -

Isolate the x in equation 1

3y = x + 54

Transpose 54

3y - 54 = x + 54 - 54

Collect like terms

3y - 54 = x

Substitute the x value into equation 2
- - - - - - - - -

2x + 6y = 0

2(3y - 54) + 6y = 0

Distributive property

6y - 108 + 6y = 0

Collect like terms

12y - 108 = 0

Transpose 108

12y - 108 + 108 = 0 + 108

Collect like terms

12y = 108

Divide both sides of the equation by 12

12y / 12 = 108 / 12

y = 108/12

y = 9

Substitute the y value into equation 2
- - - - - - - - - - - - - -

2x + 6y = 0

2x + 6(9) = 0

2x + 54 = 0

transpose 54

2x + 54 - 54 = 0 - 54

Collect like terms

2x = - 54

Divide both sides of the equation by 2

2x / 3 = - 54 / 2

x = - 54/2

x = - 27

Substitute the x value into equation 2
- - - - - - - - - -

Check for equation 2

2x + 6y = 0

2(- 27) + 6(9) = 0

- 54 + 54 = 0

0 = 0
- - - - - - - - -

Check for equation 1

3y = x + 54

3(9) = - 27 + 54

27 = 27
- - - - - - - - -

Both equations balance

The solution set ( - 27, 9)

- - - - - - s-

Answer 3

The easiest variable to get by itself is the x in the first equation
3y - 54 = x

substitute 3y - 54 in for x in the second equation

2(3y - 54) + 6y = 0
6y -108 + 6y = 0
12y = 108
y = 9

then x = 3y -54 = 3(9) - 54= 27 - 54 = -27

(-27,9)

Answer 4

2(3y - 54) + 6y = 0
12y = 108
y = 9

x = 27 - 54
x = - 27

x = - 27 , y = 9
OPTION b