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]
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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
