If 3x+2y=12 and - 4x+6y=24 what is the value of - x+2y

(1) 3x+2y=12

(2) - 4x+6y=24

Solving the system of equations using the method of substitution:

Isolating y in the first equation:

(1) 3x+2y=12→3x+2y-3x=12-3x→2y=12-3x→2y/2 = (12-3x) / 2→y = (12-3x) / 2

Replacing "y" by (12-3x) / 2 in the second equation:

(2) - 4x+6y=24

y = (12-3x) / 2→-4x+6[ (12-3x) / 2]=24

Solving for x:

-4x+3 (12-3x) = 24

-4x+36-9x=24

-13x+36=24

-13x+36-36=24-36

-13x=-12

-13x / (-13) = - 12 / (-13)

x=12/13

Replacing "x" by 12/13 in y = (12-3x) / 2

x=12/13→y=[12-3 (12/13) ]/2

y = (12-36/13) / 2

y={[ (13) (12) - 36]/13}/2

y=[ (156-36) / 13]/2

y = (120/13) / 2

y = (120/13) (1/2)

y=60/13

x=12/13; y=60/13

-x+2y=-12/13+2 (60/13)

-x+2y=-12/13+120/13

-x+2y = (-12+120) / 13

-x+2y=108/13

Answer: The value of - x+2y is 108/13