Please help me with this question

Mathematics

1 answer:

Liono4ka [1.6K]3 years ago

5 0

9514 1404 393

Answer:

(x, y) = (5, 2)

Step-by-step explanation:

Given:

LP = x

MP = 2y+3

NP = y+3

KP = 3x -8

KP = MP, LP = NP

Find:

x, y

Solution:

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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