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