Question

I'm confused regarding the elimination method for
5x - 7y = -16,
2x + 8y = 26

Answer 1

#1: 5x - 7y = -16
#2: 2x + 8y = 26

To eliminate y, multiply #1 by 8 and #2 by 7 to get

40x - 56y = -128
14x + 56y = 182

If you add those two new equations, the y's are eliminated and you get

54x = 54
x=1

Now you can go back and calculate y from one of the original equations.

Answer 2

5 x - 7 y = - 16 Multiply both sides by - 2

- 10 x + 14 y = 32


2 x + 8 y = 26 Multiply both sides by 5

10 x + 40 y = 130



- 10 x + 14 y = 32

10 x + 40 y = 130 Add equations


- 10 x + 10 x + 14 y + 40 y = 32 + 130

54 y = 162 Divide both sides by 54

y = 162 / 54 = 3


5 x - 7 y = - 16

5 x - 7 * 3 = - 16

5 x - 21 = - 16 Add 21 to both sides

5 x - 21 + 21 = - 16 + 21

5 x = 5 Divide both sides by 5

x = 1


Solutions :

x = 1 , y = 3