Questions: System A Line 1: y=1/2 x+5/2 Line 2: y=-x-2 This system of equations is: inconsistent consistent dependent consistent independent This means the system has: a unique solution Solution: , infinitely many solutions no solution System B Line 1: y=1/4 x+3 Line 2: -x+4 y=12 This system of equations is: inconsistent consistent dependent consistent independent This means the system has: a unique solution Solution: . infinitely many solutions no solution System C Line 1: y=-1/2 x Line 2: y=-1/2 x+2 This system of equations is: inconsistent consistent dependent consistent independent This means the system has: a unique solution Solution: . infinitely many solutions no solution

System A Line 1: y=1/2 x+5/2 Line 2: y=-x-2 This system of equations is: inconsistent consistent dependent consistent independent This means the system has: a unique solution Solution: , infinitely many solutions no solution System B Line 1: y=1/4 x+3 Line 2: -x+4 y=12 This system of equations is: inconsistent consistent dependent consistent independent This means the system has: a unique solution Solution: . infinitely many solutions no solution System C Line 1: y=-1/2 x Line 2: y=-1/2 x+2 This system of equations is: inconsistent consistent dependent consistent independent This means the system has: a unique solution Solution: . infinitely many solutions no solution
Transcript text: System A Line 1: $y=\frac{1}{2} x+\frac{5}{2}$ Line 2: $y=-x-2$ This system of equations is: inconsistent consistent dependent consistent independent This means the system has: a unique solution Solution: $\square$ , infinitely many solutions no solution System B Line 1: $y=\frac{1}{4} x+3$ Line 2: $-x+4 y=12$ This system of equations is: inconsistent consistent dependent consistent independent This means the system has: a unique solution Solution: $\square$ . $\square$ infinitely many solutions no solution System C Line 1: $y=-\frac{1}{2} x$ Line 2: $y=-\frac{1}{2} x+2$ This system of equations is: inconsistent consistent dependent consistent independent This means the system has: a unique solution Solution: $\square$ .]) infinitely many solutions no solution
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Solution

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Solution Steps

Step 1: Analyze System A

The two lines in System A intersect at a single point (-2, 0).

Step 2: Analyze System B

Manipulating the second equation of System B, we have:

-x + 4y = 12

4y = x + 12

y = (1/4)x + 3

This is the same as the first equation, so the lines are coincident.

Step 3: Analyze System C

The two lines in System C are parallel, having the same slope (-1/2) but different intercepts.

Final Answer

System A: consistent independent, a unique solution (-2,0)

System B: consistent dependent, infinitely many solutions

System C: inconsistent, no solution

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