Answer:
The solution to the system of equations is:
[tex]x=0,\:y=0[/tex]
Step-by-step explanation:
Given the system of equations
2x = -6y
12x + 12y = 0
solving the system of equations by elimination method
[tex]\begin{bmatrix}2x=-6y\\ 12x+12y=0\end{bmatrix}[/tex]
Arrange equation variables for elimination
[tex]\begin{bmatrix}2x+6y=0\\ 12x+12y=0\end{bmatrix}[/tex]
Multiply 2x+6y = 0 by 6: 12x+36y=0
[tex]\begin{bmatrix}12x+36y=0\\ 12x+12y=0\end{bmatrix}[/tex]
subtracting the equations
[tex]12x+12y=0[/tex]
[tex]-[/tex]
[tex]\underline{12x+36y=0}[/tex]
[tex]-24y=0[/tex]
solve -24y=0 for y
[tex]-24y=0[/tex]
divide both sides by -24
[tex]\frac{-24y}{-24}=\frac{0}{-24}[/tex]
Simplify
[tex]y=0[/tex]
For 12x+36y=0 plug in y = 0
[tex]12x+36y=0[/tex]
[tex]12x+36\cdot \:0=0[/tex]
[tex]12x+0=0[/tex]
[tex]12x=0[/tex]
Divide both sides by 12
[tex]\frac{12x}{12}=\frac{0}{12}[/tex]
Simplify
[tex]x=0[/tex]
Therefore, the solution to the system of equations is:
[tex]x=0,\:y=0[/tex]
