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20 votes
ABC is equilateral and AB = -x + 3y,

BC = 4x - y, and AC = 11. Find x and y.

Hi would you help me with this

User Ravinggenius
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1 Answer

26 votes
26 votes

Answer:

x = 4 , y = 5

Explanation:

the sides of an equilateral are congruent , then

AB = BC = 11

set up a system of equations and solve simultaneously, that is

- x + 3y = 11 → (1)

4x - y = 11 → (2)

multiplying (2) by 3 and adding to (1) will eliminate y

12x - 3y = 33 → (3)

add (1) and (3) term by term to eliminate y

11x + 0 = 44

11x = 44 ( divide both sides by 11 )

x = 4

substitute x = 4 into either of the 2 equations and solve for y

substituting into (1)

- 4 + 3y = 11 ( add 4 to both sides )

3y = 15 ( divide both sides by 3 )

y = 5

solution is x = 4 and y = 5

User Mnuzzo
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