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

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