3(x + y) = 12 (x)/(2) = 3 If (x,y) is a solution to the system of equations above, what is the value of y? A) -6 B) -2 C) 2 D) 6​

Question

3(x + y) = 12


`(x)/(2) = 3`

If (x,y) is a solution to the system of equations above, what is the value of y?
A) -6
B) -2
C) 2
D) 6​

Answer 1

B. -2.

Explanation:

3(x + y) = 12

x/2 = 3

From the second equation

x = 2*3

x = 6.

Substitute for x in the first equation:

3(6 + y) = 12

18 + 3y = 12

3y = 12 - 18

3y = -6

y = -2.

Answer 2

`\large\boxed{B)\ -2}`

Explanation:

`\left\{\begin{array}{ccc}3(x+y)=12&(1)\\\\(x)/(2)=3&(2)\end{array}\right\\\\(2)\ (x)/(2)=3\qquad\text{multiply both sides by 2}\\\\2\!\!\!\!\diagup^1\cdot(x)/(2\!\!\!\!\diagup_1)=(2)(3)\\\\x=6\\\\\text{Put it to (1):}\\\\3(6+y)=12\qquad\text{divide both sides by 3}\\\\(3\!\!\!\!\diagup^1(6+y))/(3\!\!\!\!\diagup_1)=(12)/(3)\\\\6+y=4\qquad\text{subtract 6 from both sides}\\\\6-6+y=4-6\\\\y=-2`