Question: Line 1: $y = -\frac{1}{4}x$ Line 2: $x + 4y = 0$ This system of equations is: - inconsistent -…

Line 1: $y = -\frac{1}{4}x$

Line 2: $x + 4y = 0$

This system of equations is:

• inconsistent
• consistent independent
• consistent dependent

Solution

To determine the type of system, we need to analyze the given equations and their lines. The equations are: Line 1: \( y = -\frac{1}{4}x \) Line 2: \( x + 4y = 0 \) First, solve Line 2 for \( y \). \[ x + 4y = 0 \] Subtract \( x \) from both sides: \[ 4y = -x \] Divide both sides by 4: \[ y = -\frac{1}{4}x \] Both Line 1 and Line 2 simplify to: \[ y = -\frac{1}{4}x \] Since both equations represent the same line, the system of equations is consistent and dependent.