use elimination method to find 0.3x-0.2y=4 amd 0.2+0.3y=5/23

Question

How is the answer found?

Answer 1

0.3x -0.2y = 4

0.2x +0.3y = 5/23

multiply the top equation by 3 on both sides

0.9x -0.6y = 12

0.2x +0.3y = 5/23

multiply the bottom equations by 2 on both sides

0.9x -0.6y = 12

0.4x +0.6y = 10/23

add the equations together

1.3x +0y = 12   10/23

1.3x = 286/23

(13/10)x = 286/23

x = (286/23)*(10/13)

x = (22/23)*(10/1)

x = 220/23

now look at the original equations:

0.3x -0.2y = 4

0.2x +0.3y = 5/23

multiply the top equation by 2

0.6x -0.4y = 8

0.2x +0.3y = 5/23

multiply the bottom equation by -3

0.6x -0.4y = 8

-0.6x -0.9y = -15/23

add the equations together

0x -1.3y = 8 -15/23

-1.3y = 169/23

(-13/10)y = 169/23

y = (169/23)*(-10/13)

y = (13/23)*(-10/1)

y = -130/23

Answer:  x = 220/23, y = -130/23