Question

question
determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
(-x + 3y = 3)
(x - 3y = -3)

Explanation:

Step1: Analyze the two equations

First equation: $-x + 3y = 3$
Second equation: $x - 3y = -3$

Step2: Manipulate the first equation

Multiply the first equation by $-1$:
$$-1\times(-x + 3y) = -1\times3$$
$$x - 3y = -3$$

Step3: Compare the two equations

The manipulated first equation is identical to the second equation. This means the two equations represent the same line, so every point on the line is a solution.

Answer:

The system has infinitely many solutions.