In which quadrant does the solution of the system fall?

2 Answers

• From X + Y = 4

  Y = 4 – X

  Substituite this for Y in 2X – Y = 2 to get

  2X -(4 – X ) = 2

  2X -4 +X = 2

  3X = 6

  X = 2

  Now return to X + Y = 4

  Knowing X = 2,

  2 + Y = 4

  Y = 4 – 2

  Y = 2

  The solution is (X,Y) = (2,2)

  This is quadrant I

  Answer is A

• Look at the first equation. If x + y = 4, that means x = 4 – y. We can now substitute that in for x in the second equation.

  2x – y = 2

  2*(4-y) – y = 2

  8 – 2y – y = 2

  8 – 3y = 2

  -3y = – 6

  y = 2

  And since we know x + y = 4, x = 2. So the solution is (2,2), which is in quadrant 1.