Question

Sam bought 2 model airplanes and 6 toy cars. He paid $17 total. Marissa bought 2 model airplanes and returned 10 toy cars. She paid $9 total. A system of equations that represents their purchases and returns is shown below, where x represents the cost of a model airplane and y represents the cost of a toy car.

2x+6y=17
2x-10y=9

Select the equations that could represent 2x+6y=17 and still produce the same answer to the system of equations, if 2x+(-10y)=9 were multiplied by 2 and added to 2x+6y=1

A. 6x-14y=35

B. 4x+12y=-34

C. x-16y=26

D. -2x+26y=-1

Answer 1

Just figuring the first term is sufficient to let you chose the correct answer. It is easy enough to do the entire operation requested.
  2(2x -10y) +(2x +6y) = 2(9) +(17)
  4x -20y +2x +6y = 18 +17 . . . . . . . eliminate parentheses
  6x -14y = 35 . . . . . . . . . . . . . . . . . matches A. 6x-14y=35