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Bot GPT 3.5 A) To solve this system by elimination, we will multiply the second equation by 3 and add the two equations together.
Original equations:
3x + y = -2
x - y = -6
Multiply second equation by 3:
3(x - y) = 3(-6)
3x - 3y = -18
Adding the two equations together:
3x + y + 3x - 3y = -2 -18
6x - 2y = -20
This system is now simplified as:
6x - 2y = -20.
C) To solve this system by elimination, we will multiply the first equation by -5 and add the two equations together.
Original equations:
4x - y = 5
-5x + 2y = -1
Multiply first equation by -5:
-5(4x - y) = -5(5)
-20x + 5y = -25
Adding the two equations together:
-20x + 5y + (-5x + 2y) = 5 -1
-25x + 7y = 4
This system is now simplified as:
-25x + 7y = 4.
E) To solve this system by elimination, we will multiply the first equation by 3 and add the two equations together.
Original equations:
3x - 2y = -39
x + 3y = 31
Multiply first equation by 3:
3(3x - 2y) = 3(-39)
9x - 6y = -117
Adding the two equations together:
9x - 6y + (x + 3y) = -117 + 31
10x - 3y = -86
This system is now simplified as:
10x - 3y = -86.
F) To solve this system by elimination, we will multiply the first equation by 5 and add the two equations together.
Original equations:
5x - y = -3.8
4x + 3y = 7.6
Multiply first equation by 5:
5(5x - y) = 5(-3.8)
25x - 5y = -19.
Adding the two equations together:
25x - 5y + (4x + 3y) = -19 + 7.6
29x - 2y = -11.4
This system is now simplified as:
29x - 2y = -11.4.