Question

{2x
x = -6y
12x + 12y = 0
Solve the system of equations.

Answer 1

The solution to the system of equations is:

`x=0,\:y=0`

Explanation:

Given the system of equations

2x = -6y

12x + 12y = 0

solving the system of equations by elimination method

`\begin{bmatrix}2x=-6y\\ 12x+12y=0\end{bmatrix}`

Arrange equation variables for elimination

`\begin{bmatrix}2x+6y=0\\ 12x+12y=0\end{bmatrix}`

Multiply 2x+6y = 0 by 6: 12x+36y=0

`\begin{bmatrix}12x+36y=0\\ 12x+12y=0\end{bmatrix}`

subtracting the equations

`12x+12y=0`

`-`

`\underline{12x+36y=0}`

`-24y=0`

solve -24y=0 for y

`-24y=0`

divide both sides by -24

`(-24y)/(-24)=(0)/(-24)`

Simplify

`y=0`

For 12x+36y=0 plug in y = 0

`12x+36y=0`

`12x+36\cdot \:0=0`

`12x+0=0`

`12x=0`

Divide both sides by 12

`(12x)/(12)=(0)/(12)`

Simplify

`x=0`

Therefore, the solution to the system of equations is:

`x=0,\:y=0`