3) \( \begin{array}{l}y \\ =-\frac{1}{2} x-1 \\ y\end{array}=\frac{1}{4} x-4 \)

To solve the system of equations, we can set the two equations equal to each other since they both equal \( y \): \[ -\frac{1}{2} x - 1 = \frac{1}{4} x - 4 \] Now, let's gather the \( x \) terms on one side and the constant terms on the other. Start by adding \( \frac{1}{2} x \) to both sides, which gives us: \[ -1 = \frac{1}{4} x + \frac{1}{2} x - 4 \] To combine the \( x \) terms, convert \( \frac{1}{2} x \) to fourths: \[ \frac{1}{2} x = \frac{2}{4} x \] Now, substituting back into the equation: \[ -1 = \frac{3}{4} x - 4 \] Next, add 4 to both sides: \[ 3 = \frac{3}{4} x \] To isolate \( x \), multiply both sides by \(\frac{4}{3}\): \[ x = 4 \] Now, substitute \( x = 4 \) back into one of the original equations to find \( y \). Using the first equation: \[ y = -\frac{1}{2}(4) - 1 = -2 - 1 = -3 \] Thus, the solution to the system of equations is: \[ (x, y) = (4, -3) \] So, the point of intersection is \( (4, -3) \).