Question

system a

line 1: \\(y = 3x - 3\\)
line 2: \\(-3x + y = -3\\)

this system of equations is:

• inconsistent
• consistent independent
• consistent dependent

this means the system has:

• a unique solution

solution: \\((\quad, \quad)\\)

• infinitely many solutions
• no solution

system b

line 1: \\(y = 2x - 1\\)
line 2: \\(y = -2x - 1\\)

this system of equations is:

• inconsistent
• consistent independent
• consistent dependent

this means the system has:

• a unique solution

solution: \\((\quad, \quad)\\)

• infinitely many solutions
• no solution

system c

line 1: \\(y = \frac{2}{3}x + 1\\)
line 2: \\(y = \frac{2}{3}x - 2\\)

this system of equations is:

• inconsistent
• consistent independent
• consistent dependent

this means the system has:

• a unique solution

solution: \\((\quad, \quad)\\)

• infinitely many solutions
• no solution

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: consistent independent
• This means the system has: a unique solution
• Solution: \((0, -1)\)

Question 3: System C

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