Solve each system by using elimination.

Question

A) 3x + y = -2 C) 4x - y = 5 E) 3x - 2y = -39 F) 5x - y = -3.8
x - y = -6 -5x + 2y = -1 x + 3y = 31 4x + 3y = 7.6

Answer 1

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.