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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.

_____

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.