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kicyunya [14]
2 years ago
11

Please help me with this question

Mathematics
1 answer:
Liono4ka [1.6K]2 years ago
5 0

9514 1404 393

Answer:

  (x, y) = (5, 2)

Step-by-step explanation:

<u>Given</u>:

  LP = x

  MP = 2y+3

  NP = y+3

  KP = 3x -8

  KP = MP, LP = NP

<u>Find</u>:

  x, y

<u>Solution</u>:

The given relations between the segment lengths let us write two equations:

  KP = MP

  3x -8 = 2y +3   ⇒   3x -2y -11 = 0   [eq1]

  LP = NP

  x = y +3   ⇒   x -y -3 = 0   [eq2]

__

Subtracting 3 times [eq2] from [eq1] gives ...

  (3x -2y -11) -3(x -y -3) = 0

  y -2 = 0 . . . . . . . . simplify

  y = 2 . . . . . . . . . . add 2

Substituting this value into [eq2] gives ...

  x = 2 + 3 = 5

The values of x and y are ...

  x = 5, y = 2

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