Solve the system by elimination

9514 1404 393

  5)  (x, y) = (10, -1)

  6)  (x, y) = (5, 6)

Step-by-step explanation:

5) y coefficients are opposites, so y can be eliminated by adding the two equations.

  (x -y) +(2x +y) = (11) +(19)

  3x = 30 . . . . . simplify

  x = 10 . . . . . . . divide by 3

Using the second equation, we can find y:

  2(10) +y = 19

  y = -1 . . . . . subtract 20

The solution is (x, y) = (10, -1).

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6) The x-coefficients are the same, so we can eliminate the x-term by subtracting the second equation from the first. We choose to do it that way so the y-coefficient ends up positive.

  (-6x +6y) -(-6x +3y) = (6) -(-12)

  3y = 18 . . . . . . simplify

  y = 6 . . . . . . . . divide by 6

Using the first equation to find x, we have ...

  -6x +6(6) = 6

  x -6 = -1 . . . . . . . divide by -6

  x = 5 . . . . . . . . . add 6

The solution is (x, y) = (5, 6).