Question

system a
line 1: \\(y = \frac{2}{3}x + 1\\)
line 2: \\(y = \frac{2}{3}x + 4\\)
this system of equations is:

• consistent dependent
• consistent independent
• inconsistent

this means the system has:

• a unique solution

solution: \\((\text{ },\text{ })\\)

• no solution
• infinitely many solutions

system b
line 1: \\(y = x + 3\\)
line 2: \\(y = \frac{1}{2}x + \frac{5}{2}\\)
this system of equations is:

• consistent dependent
• consistent independent
• inconsistent

this means the system has:

• a unique solution

solution: \\((\text{ },\text{ })\\)

• no solution
• infinitely many solutions

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

• consistent dependent
• consistent independent
• inconsistent

this means the system has:

• a unique solution

solution: \\((\text{ },\text{ })\\)

• no solution
• infinitely many solutions

Explanation:

Analyze System A

$$
LATEXBLOCK0
$$

Analyze System B

$$
LATEXBLOCK1
$$

Analyze System C

$$
LATEXBLOCK2
$$

Answer:

Question 1: System A

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

Question 2: System B

• This system of equations is: consistent independent
• This means the system has: a unique solution
• Solution: \((-1, 2)\)

Question 3: System C

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