Question

x - y = -1
y = -4x - 4
which describes the system of equations above?
consistent and dependent
consistent and independent
inconsistent

Explanation:

Step1: Substitute \( y = -4x - 4 \) into \( x - y = -1 \)

Substitute \( y \) in the first equation: \( x - (-4x - 4) = -1 \)
Simplify the left - hand side: \( x + 4x+4=-1 \)
Combine like terms: \( 5x + 4=-1 \)

Step2: Solve for \( x \)

Subtract 4 from both sides: \( 5x=-1 - 4=-5 \)
Divide both sides by 5: \( x=\frac{-5}{5}=-1 \)

Step3: Solve for \( y \)

Substitute \( x = - 1 \) into \( y=-4x - 4 \)
\( y=-4\times(-1)-4 = 4 - 4=0 \)

Step4: Determine the type of system

Since we have a unique solution (\( x=-1,y = 0 \)), a system with at least one solution is consistent. And since the two equations represent two distinct lines (because their slopes are different: for \( x - y=-1\) or \( y=x + 1\), the slope is 1; for \( y=-4x - 4\), the slope is - 4), the system is consistent and independent.

Answer:

consistent and independent