Question

x + 3y = 0\
4x - 6y = 0

Explanation:

Step1: Simplify the second equation

We have the system of equations:
\[

$$\begin{cases} x + 3y = 0 \\ 4x - 6y = 0 \end{cases}$$

\]
Divide the second equation \(4x - 6y = 0\) by 2, we get \(2x - 3y = 0\).

Step2: Add the two equations

Now we have the first equation \(x + 3y = 0\) and the simplified second equation \(2x - 3y = 0\). Add them together:
\((x + 3y)+(2x - 3y)=0 + 0\)
Simplify the left - hand side: \(x+2x+3y - 3y=3x\), and the right - hand side is 0. So \(3x = 0\), which implies \(x = 0\).

Step3: Substitute x into the first equation

Substitute \(x = 0\) into the first equation \(x+3y = 0\). We get \(0 + 3y=0\), then \(3y=0\), so \(y = 0\).

Answer:

The solution of the system of equations is \(x = 0,y = 0\) (the solution is the point \((0,0)\)).