4x + y = 7x and 2x + 3y = x

The first equation is $4x + y = 7x$.
Subtract $4x$ from both sides to isolate $y$:

$$y = 7x - 4x$$ $$y = 3x \quad (*)$$

The second equation is $2x + 3y = x$.
Subtract $2x$ from both sides:

$$3y = x - 2x$$ $$3y = -x \quad (**)$$

Substitute $y = 3x$ from equation $(*)$ into equation $(**)$:

$$3(3x) = -x$$ $$9x = -x$$

Add $x$ to both sides of the equation:

$$9x + x = 0$$ $$10x = 0$$

Divide by 10:

$$x = \frac{0}{10}$$ $$x = 0$$

Using $y = 3x$:

$$y = 3(0)$$ $$y = 0$$

The solution to the system of equations is:

$$x = 0$$ $$y = 0$$ $$x=0, y=0$$