Question

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

• consistent independent
• consistent dependent
• inconsistent

this means the system has:

• a unique solution

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

• infinitely many solutions
• no solution

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

• consistent independent
• consistent dependent
• inconsistent

this means the system has:

• a unique solution

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

• infinitely many solutions
• no solution

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

• consistent independent
• consistent dependent
• inconsistent

this means the system has:

• a unique solution

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

• infinitely many solutions
• no solution

Explanation:

Analyze the first system of equations

$$
LATEXBLOCK0
$$

Analyze the second system of equations

$$
LATEXBLOCK1
$$

Analyze the third system of equations

$$
LATEXBLOCK2
$$

Answer:

Question 1 (Left Column)

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

Question 2 (Middle Column)

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

Question 3 (Right Column)

• This system of equations is: consistent independent
• This means the system has: a unique solution
• Solution: \((0, 2)\)