Question

Coordinate grid with plotted ordered pairs, point A at negative 5, 4 point B at 4, 7 point C at negative 2, 7 point D at negative 7, 1 point E at 4, negative 2 point F at 1, negative 6 point G at negative 3, negative 10 point H at negative 4, negative 4 point I at 9, 3 point J at 7, negative 4 and point K at 2, 3
The coordinate grid shows points A through K. Which points are solutions to the system of inequalities listed below?

2x + y ≤ 10
2x − 4y < 8

Answer 1

A graph shows points A, C, D, K are in the solution set.

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Doing all the calculations is fairly tedious, but can be done manually. (It works better, perhaps, to do it on a spreadsheet.) It is convenient to reduce the second equation by a factor of 2 to
    x -2y < 4

  point A(-5, 4) in the first equation: 2(-5)+(4) = -2 ≤ 10
  point A(-5, 4) in the second (reduced) equation: (-5)-2(4) = -13 < 4

  point H(-4, -4) in the first equation: 2(-4) +(-4) = -12 ≤ 10
  point H(-4, -4) in the second equation: (-4) -2(-4) = 4 < 4 . . . FALSE