Questions: y=1/2 x-2 y=-x-5 This system of equations is: inconsistent consistent dependent consistent independent This means the system has: y=3/2 x+3 -3 x+2 y=6 This system of equations is: inconsistent consistent dependent consistent independent This means the system has: y=5/2 x+3 y=5/2 x-4 This system of equations is: inconsistent consistent dependent consistent independent This means the system has:

y=1/2 x-2

y=-x-5

This system of equations is:
inconsistent
consistent dependent
consistent independent
This means the system has:

y=3/2 x+3

-3 x+2 y=6

This system of equations is:
inconsistent
consistent dependent
consistent independent
This means the system has:

y=5/2 x+3

y=5/2 x-4

This system of equations is:
inconsistent
consistent dependent
consistent independent
This means the system has:

Transcript text: $y=\frac{1}{2} x-2$ $y=-x-5$ This system of equations is: inconsistent consistent dependent consistent independent This means the system has: $y=\frac{3}{2} x+3$ $-3 x+2 y=6$ This system of equations is: inconsistent consistent dependent consistent independent This means the system has: $y=\frac{5}{2} x+3$ $y=\frac{5}{2} x-4$ This system of equations is: inconsistent consistent dependent consistent independent This means the system has:

Solution

Solution Steps

Step 1: Identify the type of system for the first set of equations

Equations:
- Line 1: $ y = \frac{1}{2}x - 2 $
- Line 2: $ y = -x - 5 $
Graph Analysis: The lines intersect at one point.
Conclusion: The system is consistent and independent.

Step 2: Identify the type of system for the second set of equations

Equations:
- Line 1: $ y = \frac{3}{2}x + 3 $
- Line 2: $ -3x + 2y = 6 $
Graph Analysis: The lines are the same (coincident).
Conclusion: The system is consistent and dependent.

Step 3: Identify the type of system for the third set of equations

Equations:
- Line 1: $ y = \frac{5}{2}x + 3 $
- Line 2: $ y = \frac{5}{2}x - 4 $
Graph Analysis: The lines are parallel and do not intersect.
Conclusion: The system is inconsistent.