How the witches play a central role in shifting only macbeth and how he chang throught the play

Macbeth's character changes a lot from the beginning to the end of the play. At first he's a respected Thane who is, at least shows himself to be, loyal to King Duncan. But he gets ambitious (greedy is a better term, but I don't remember the whole play). Lady Macbeth doesn't help, nor does the prophecy he heard sometime during the play help either. He decides to murder King Duncan to seize the throne, but because of his guilt and fear out of betrayal, he goes on a murdering spree. He is then killed at the end by Macduff, who was not "woman born."

The witches, or "weird sisters," as they are often called, play a pivotal role in Macbeth. Macbeth himself is obsessed with their prophecies, and repeatedly consults with them. After discovering the prophecy, he then makes the decision to kill Duncan. This is the beginning of the downfall of his character.  Soon after, to fulfill the prophecy he orders the death of his friend Banquo and son. This brings about the hallucinations and insanity. Thanks to the witches he believes he is immortal. We know very little about the true identity of the witches; however, their role is clear, they are Fate. The witches weave their way into Macbeth's life clearly to change destiny and toy with his future and destroy humanity. Without the witches, Macbeth would not have started on the dark path of murder and despair.

substitute y = 2x - 4 to x + 2y = 12:

x + 2(2x - 4) = 12     use distributive property

x + (2)(2x) + () = 12

x + 4x - 8 = 12     add 8 to both sides

5x = 20     divide both sides by 5

x = 4

put the value of x to the first equation:

y = 2(4) - 4

y = 8 - 4

y = 4

1)a

2 b

3 d

4 d or b

explanation: