System A : consistent dependent.
System B : no solution.
System C: consistentent independent and its solution is (-3, -2).
STEP - BY - STEP EXPLANATION
What to find?
To tell whether the system given is;
inconsistent, consistent dependent or consistent independent.
Given:
• System A
y = 1/4 x - 4
-x + 4y = -16
• System B
y=2/3 x + 2
y = 2/3 x + 3
• System C
y = -x - 5
y=2x + 4
To be able to decribe the given systems, we will:
• Define the terminologies
,
• Observe the given graph
,
• Identify the graph.
Inconsistent
If a system has no solution, it is said to be inconsistent . The graphs of the lines do not intersect, so the graphs are parallel and there is no solution.
Observe the graph of system B,
The lines are parallel and hence the system has no solution.
Consistent dependent
If a system has at least one solution, it is said to be consistent .
If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line.
Observe the graph of system A, the lines are the same.
Hence, the system of the equation in A is consistent dependent.
Consistent independent
If a system has at least one solution, it is said to be consistent .
If a consistent system has exactly one solution, it is independent . In this case the point of intersection of the line line on the graph is only at one point.
Observe the graph of system C, the line iontercsect at only one point which implies the system has exactly one solution at that point.
Therefore, system C can be decribed as consistent independent
and its solution is (-3, -2).