Question

Find the value of y in the solution to the system of equations shown.

Answer 1

• 3y=18x+6

Divide by 3

• y=6x+2--(1)
• y=2x+14--(2)

Equating

• 6x+2=2x+14
• 4x=12
• x=3

Now

• y=6(3)+2
• y=18+2
• y=20

C

Answer 2

Answer:

C.  y = 20

Step-by-step explanation:

Given system of equations:

$\begin{cases}3y = 18x + 6\\y = 2x + 14\end{cases}$

Multiply the second equation by 3:

$\implies (3)y=(3)2x+(3)14$

$\implies 3y=6x+42$

Subtract this from the first equation to eliminate 3y:

$\begin{array}{r l}3y & = 18x+6\\-\quad3y&=6x+42\\\cline{1-2}0&=12x-36\end{array}$

Solve the resulting equation for x:

$\implies 12x-36=0$

$\implies 12x=36$

$\implies x=3$

Substitute the found value of x into the original second equation and solve for y:

$\implies y=2(3)+14$

$\implies y=6+14$

$\implies y=20$