Question

for each system of linear equations shown below, classify the system as \consistent dependent,\ \consistent independent,\ or \inconsistent.\ choose the best description of its solution. if the system has exactly one solution, give its solution.

system a
line 1: \\(y = -x + 4\\)
line 2: \\(x + y = 4\\)
this system of equations is:

• consistent independent
• consistent dependent
• inconsistent

this means the system has:

system b
line 1: \\(y = x\\)
line 2: \\(y = x - 4\\)
this system of equations is:

• consistent independent
• consistent dependent
• inconsistent

this means the system has:

system c
line 1: \\(y = 2x - 1\\)
line 2: \\(y = -\frac{1}{2}x + \frac{3}{2}\\)
this system of equations is:

• consistent independent
• consistent dependent
• inconsistent

this means the system has:

Explanation:

Analyze System A

$$
LATEXBLOCK0
$$

Analyze System B

$$
LATEXBLOCK1
$$

Analyze System C

$$
LATEXBLOCK2
$$

Answer:

Question 1 (System A)

• This system of equations is: consistent dependent
• This means the system has: infinitely many solutions

Question 2 (System B)

• This system of equations is: inconsistent
• This means the system has: no solution

Question 3 (System C)

• This system of equations is: consistent independent
• This means the system has: exactly one solution
• Solution: \((1, 1)\)