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Sagot :

Answer:

  • x +2y -1 = 3, x -4y +6 = 7
  • x = 3, y = 1/2

Step-by-step explanation:

(a)

The left side and the right side of the kite are equal lengths, so each is half the perimeter. That means AB = AD = 3, since half the perimeter is 10, and CB = CD = 7.

The two equations can be ...

  AB = 3

  x +2y -1 = 3

  CB = 7

  x -4y +6 = 7

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(b)

Subtracting the second from the first gives ...

  (x +2y -1) -(x -4y +6) = (3) -(7)

  6y -7 = 3 -7 . . . . simplify

  6y = 3 . . . . . . . . add 7

  y = 3/6 = 1/2 . . . . divide by 6

  x +2(1/2) -1 = 3 . . . . substitute for y in the first equation

  x = 3 . . . . . . . . simplify

The values of x and y are 3 and 1/2, respectively.

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Additional comment

We could collect the constants in the equations so they were all on the same side of the equal sign. As we saw above, that is not necessary.