Question

line 1: $y = \frac{1}{2}x - 1$
line 2: $y = x - 1$
image of a coordinate plane with two lines l1 and l2
this system of equations is:
\circ inconsistent
\circ consistent independent
\circ consistent dependent
this means the system has:
\circ a unique solution
solution: ( , )

Explanation:

Step1: Compare slopes of lines

Line 1 slope: $m_1=\frac{1}{2}$, Line 2 slope: $m_2=1$

Step2: Analyze system type

Distinct slopes mean lines intersect once. A system with exactly one intersection is consistent independent, with a unique solution.

Step3: Find intersection (verify)

Set $\frac{1}{2}x - 1 = x - 1$
Subtract $\frac{1}{2}x$: $-1 = \frac{1}{2}x - 1$
Add 1: $0 = \frac{1}{2}x$ → $x=0$
Substitute $x=0$ into $y=x-1$: $y=-1$
Intersection at $(0,-1)$, one unique solution.

Answer:

This system of equations is: consistent independent
This means the system has: a unique solution
Solution: $(0, -1)$