Solve System: (x+3y)/2 = 0 and x+y = 4

To solve this system of linear equations, we'll employ the substitution method. The equations given are:

$\frac{x+3y}{2} = 0$

$x + y = 4$

Step 1: Solve the first equation for $x$.

The equation $\frac{x+3y}{2} = 0$ can be simplified:

Multiply both sides by 2 to eliminate the fraction:

$x + 3y = 0$

Solving for $x$, we get:

$x = -3y$

Step 2: Substitute this expression for $x$ into the second equation.

Substitute $x = -3y$ into $x + y = 4$:

$-3y + y = 4$

This simplifies to:

$-2y = 4$

Step 3: Solve for $y$.

Divide both sides by -2 to find $y$:

$y = -2$

Step 4: Substitute $y = -2$ back into the expression for $x$.

Using $x = -3y$:

$x = -3(-2) = 6$

Thus, the solution to the system of equations is $x = 6$ and $y = -2$.

Therefore, the solution to the problem is $x = 6, y = -2$.