Question

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

3y = 18x + 6
y = 2x + 14

A. y = 3
B. y = 4
C. y = 20
D. y = 26

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

C. y = 20

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`